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IIT JEE circle hyperbola common tangent part 1 | Conic sections | Algebra II | Khan Academy

Video vocabulary

problem

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US / ˈprɒbləm /

UK / ˈprɑbləm /

A1
  • adjecitve
  • Causing trouble
  • noun
  • Something difficult to deal with or causes trouble
  • Question to show understanding of a math concept

review

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US / rɪˈvju: /

UK / rɪˈvju /

A2
  • noun
  • Examination of soldiers and supplies
  • Opinion, as in a paper, about movie, book, or play
  • Studying again to remind yourself about something
  • verb
  • To carefully look at the quality of something
  • To formally examine something in the military
  • To write an opinion about movie, book, or play
  • To study again to remind yourself about something

could

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US / kəd /

UK / kʊd /

A1
  • other
  • Past form of 'can' to mean have ability
  • Used to ask for something politely, or to offer

complete

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US / kəm'pli:t /

UK / kəmˈplit /

A1
  • adjecitve
  • Being finished; done; achieved
  • Being as perfect and as total as could be
  • verb
  • To finish or reach the end of doing something

slightly

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US / ˈslaɪtli /

UK / ˈslaɪtli /

B1
  • adverb
  • Only a little

negative

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US / 'neɡətɪv /

UK / ˈnɛɡətɪv /

A2
  • adjecitve
  • Being harmful, unwanted or unhelpful
  • In mathematics, being less than zero
  • Focusing on the bad aspects; pessimistic
  • noun
  • The opposite to a positive electrical charge
  • In grammar, containing words such as 'no' or 'not'
  • Reply to a question or statement that means 'no'
  • Image on camera film used to make a photo

low

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US / ləʊ /

UK / lo /

A1
  • adjecitve
  • Having a small quantity, supply, or amount
  • Being unhappy or unpleasant in attitude
  • Not high; being near the ground, or bottom
  • (Of a voice, sound) being soft; quiet
  • noun
  • Situation of not having a lot of something

way

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US / weɪ /

UK / we /

A1
  • adverb
  • Used to emphasize the amount of something
  • noun
  • Particular aspect of something being thought about
  • One of various choices that could be made
  • Particular existing condition or state
  • (Often long) distance or length of time
  • How something is done
  • Route to go to a place
  • Small street
  • Usual behavior, emotions or habits of someone

common

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US / 'kɒmən /

UK / ˈkɑmən /

A1
  • adjecitve
  • Shared; Belonging to or used by everyone
  • Typical, normal; not unusual
  • noun
  • Area in a city or town that is open to everyone
  • Field near a village owned by the local community

its

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US / ɪts /

UK / ɪts /

A1
  • adjecitve
  • Referring to or belonging to ‘it’
  • determiner
  • Of something; belonging or related to something
  • other
  • Possessive form of “it”

top

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US / tɒp /

UK / tɑp /

A1
  • adjecitve
  • Being good or great; excellent
  • Being the most in degree or quality
  • noun
  • Item of clothing covering shoulders to waist, hips
  • A cover or lid
  • Part (e.g. road) that is the furthest away
  • Highest or upper part or point of something
  • Best or highest status or position
  • Flat upper surface or edge of an object
  • Child's toy that spins on its point
  • Upper section or leaves of fruits and vegetables
  • Winning in a sport or contest
  • verb
  • To be higher or larger than a specific value
  • To arrive at the highest point of something
  • To put a cover or layer or over something
  • To kill; murder
  • To hold the highest position on a list
  • To be more important, successful or better than
  • To beat someone or win at a game

comma

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US / ˈkɒmə /

UK / ˈkɑ:mə /

B2
  • noun
  • Mark showing a pause or list in a sentence

work

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US / wɜ:k /

UK / wɚk /

A1
  • adjecitve
  • Activity completed in order to make money
  • noun
  • The product of some artistic or literary endeavor
  • Everything created by an author, artist, musician
  • Activity you do in order to make money
  • Place of employment
  • Final product or result of a some labor or effort
  • verb
  • To bring into a specific state of success
  • To be functioning properly, e.g. a car
  • To do your job in your company or workplace
  • To make an effort to do something
  • To operate a machine or device

bit

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US / bɪt /

UK / bɪt /

A1
  • noun
  • Device put in a horse's mouth to control it
  • Small piece of something
  • verb
  • (E.g. of fish) to take bait and be caught

look

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US / lʊk /

UK / lʊk /

A1
  • noun
  • Person's beauty or physical attractiveness
  • Particular style of dress, clothes, or appearance
  • The way someone, something appears to be
  • Act of searching for or examining something
  • verb
  • To appear to be; seem

add

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US / æd /

UK / æd /

A1
  • verb
  • To include as well
  • To put two things or numbers together, e.g. 2+2

take

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US / teɪk /

UK / tek /

A1
  • noun
  • Filming of a single scene for TV or the movies
  • verb
  • To accept something that is offered
  • To use a method of traveling, e.g. a bus or train
  • To use a camera to make (a photo)
  • To pick up something and go away with it
  • To study a subject in school
  • To attempt to pass (an exam)
  • To require a certain amount of time, money, space

tempting

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US / ˈtemptɪŋ /

UK / ˈtɛmptɪŋ /

A2
  • verb
  • To make someone want something even if it's bad

into

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US / 'ɪntə /

UK / ˈɪntu /

A1
  • preposition
  • Moving or going inside something
  • In the same direction as; in the direction of
  • So as to become; taking the state of

perfect

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US / 'pɜ:fɪkt /

UK / ˈpɚfɪkt /

A1
  • adjecitve
  • So good it cannot be improved
  • verb
  • To do something so well, it cannot be done better

other

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US / 'ʌðə(r) /

UK / ˈʌðər /

A1
  • adjecitve
  • A thing different from that mentioned
  • determiner
  • (Something) else; not the first (one)
  • pronoun
  • Being the one and only thing of that category

open

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US / 'əʊpən /

UK / ˈopən /

A1
  • adjecitve
  • Available for use; accessible
  • Not being hidden; available for others to see
  • Being available for customers to enter or use
  • Allowing everyone to use or take part in
  • Not secret anymore
  • Not closed or shut
  • Willing to accept new ideas and thoughts
  • noun
  • Name for a tennis or golf competition
  • verb
  • To make accessible or able to be used, e.g. road
  • To start the activities or services of a business
  • To make a space or hole appear in something
  • To move or change so that it is no longer closed
  • To start something, e.g. a new business

than

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US / ðən /

UK / ðən /

A1
  • conjunction
  • Used to compare two things that are not equal

turn

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US / tɜ:n /

UK / tɚn /

A1
  • noun
  • Place where changing of direction happens
  • Your time or chance to perform a duty
  • Your chance to play or do in say a game
  • Unexpected change, as in the weather
  • verb
  • To become (a particular age)
  • To become a different quality, color, etc.
  • To change the direction of something, e.g. a car
  • To move in an opposite direction or position
  • To shape metal with a spinning tool

half

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US / hɑ:f /

UK / hæf, hɑf /

A1
  • adjecitve
  • Not complete
  • adverb
  • Partly; somewhat
  • noun
  • One of two equal periods of game time in a sport
  • The part you get when one is divided into two;

how

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US / haʊ /

UK / haʊ /

A1
  • adjecitve
  • To what degree? in what amount?
  • adverb
  • (Used to explain the way to do something)
  • exclamation
  • For what purpose or reason?
  • (Used to ask someone or something's condition)

you

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US / jʊ /

UK / ju /

A1
  • pronoun
  • Person someone is speaking or writing to
  • Person or people in general

little

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US / 'lɪtl /

UK / ˈlɪtl /

A1
  • adjecitve
  • Being short in length of time
  • Not great in size, amount, or degree; small
  • Being very young or younger than others
  • adverb
  • By an amount or degree that is not very much
  • Not often; rarely
  • noun
  • A person's name

let

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US / let /

UK / lɛt /

A1
  • verb
  • To allow someone to do something
  • Introducing a suggestion to do something together
  • To rent a house, etc. to others

might

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US / maɪt /

UK / maɪt /

A1
  • other
  • Used to politely request an action
  • Used to express that something could happen
  • Power, strength, force or influence

the

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US / ðə /

UK / ðə /

A1
  • article
  • Used to refer to something already mentioned
  • Used to show there is only one of something
  • determiner
  • Used to describe all of a family

visualization

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US / ˌvɪʒʊəlaɪ'zeɪʃn /

UK / ˌvɪʒʊəlɪˈzeʃən /

C1
  • noun
  • Act of creating an image in your mind

this

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US / ðɪs /

UK / ðɪs /

A1
  • adjecitve
  • Used to indicate something already been discussed
  • Used to indicate something happening around now
  • adverb
  • An indication by a physical motion or gesture
  • A specific amount of
  • determiner
  • Person, thing, or idea near you
  • pronoun
  • Person, thing that has already been discussed

able

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US / 'eɪbl /

UK / ˈebəl /

A2
  • adjecitve
  • Skilled; good at something
  • Having the ability to do something

multiple

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US / ˈmʌltɪpl /

UK / ˈmʌltəpəl /

B1
  • adjecitve
  • Having or involving more than one of something
  • noun
  • Number produced by multiplying a smaller number
  • Shop with many branches

term

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US / tɜ:m /

UK / tɚm /

A1
  • noun
  • Conditions applying to an agreement, contract
  • Length of time something is expected to happen
  • Fixed period of weeks for learning at school
  • The (precise) name given to something
  • verb
  • To call; give a name to

make

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US / meɪk /

UK / mek /

A1
  • noun
  • Product made by a particular company; brand
  • verb
  • To arrange or prepare something e.g. dinner
  • To get to (a place) on time
  • To gain the status of (teacher, lawyer, etc.)
  • To create something by putting things together
  • To earn a certain amount of money at a job
  • To cause or force a person to do something
  • To cause something to happen or be formed

order

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US / 'ɔ:də(r) /

UK / ˈɔrdɚ /

A1
  • noun
  • Religious or social group, as of nuns
  • Instructions to others to do what you want
  • State in which things are neat and organized
  • What you ask to buy, e.g. food in restaurant
  • Social or political control of an area
  • verb
  • To put things in a sequence, e.g. a, b, c
  • To give instructions to others to do what you want
  • To ask for something you want to buy, e.g. a meal

just

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US / dʒʌst /

UK / dʒʌst /

A1
  • adjecitve
  • Proper or appropriate; as is deserved
  • Doing or being what is right or fair
  • Legally correct; having enough evidence
  • adverb
  • Almost; nearly
  • Exactly at the time of
  • Exactly (the same as, like)

section

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US / 'sekʃn /

UK / ˈsɛkʃən /

B1
  • noun
  • A part of a whole
  • Specific area or region within a larger place
  • Specific group of people from a larger group
  • Part of a book, newspaper, etc.
  • verb
  • To divide something into smaller parts

figure

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US / ˈfiɡə /

UK / ˈfɪɡjɚ /

A1
  • noun
  • Your body shape
  • Numbers in a calculation
  • Doll-like thing meant to represent a person
  • Picture or diagram giving information in a text
  • Person who is very important or famous
  • Shape of a person seen indistinctly or in outline
  • Amount that is expressed in numbers
  • verb
  • To appear in a game, play or event
  • To calculate how much something will cost
  • To understand after thinking; work out

else

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US / els /

UK / ɛls /

A1
  • adverb
  • Otherwise; if you fail to
  • (Of person place thing etc.) besides; in addition

space

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US / speɪs /

UK / spes /

A1
  • noun
  • Empty area kept for a specific reason, like a car
  • Empty area with nothing in it
  • Area in the sky where the stars are
  • Area between written words on a page
  • verb
  • To make a certain distance or time between

approach

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US / ə'prəʊtʃ /

UK / əˈprəʊtʃ /

A2
  • noun
  • Means of reaching a place, often a road or path
  • Request of someone with a specific goal in mind
  • Specific way to handle a project, task, problem
  • verb
  • To get close to reaching something or somewhere
  • To request someone to do something specific

both

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US / bəuθ /

UK / boθ /

A1
  • determiner
  • Used to refer to two things at the same time
  • pronoun
  • Used to refer to two things at the same time

very

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US / 'verɪ /

UK / ˈvɛri /

A1
  • adjecitve
  • Concerning a large degree or amount
  • adverb
  • A lot; much; many
  • Used to stress or emphasize a noun

they

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US / ðeɪ /

UK / ðe /

A1
  • pronoun
  • Two or more people, animals, or things

center

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US / 'sentə /

UK / ˈsɛntɚ /

A1
  • noun
  • Community place people go health or social reasons
  • Place in the middle of something
  • Person or thing that is attracting attention
  • verb
  • To direct focus toward something

part

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US / pɑ:t /

UK / pɑ:rt /

A1
  • adjecitve
  • To some degree; half; not fully
  • noun
  • Division of a book
  • Ratio of something, e.g. 3 of gin, 1 of tonic
  • A line in a person's hair, made with a comb
  • Character an actor plays on stage, movie, or TV
  • Some, but not all of a specific thing
  • Role in causing something to happen
  • verb
  • To make a line in a person's hair, by using a comb
  • To move two things apart creating a space
  • To leave someone, or to break off a relationship

have

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US / həv /

UK / hæv /

A1
  • verb
  • To drink, smoke, eat or use something
  • To experience the effects of something
  • To organize an event, or join in an activity
  • To own, possess, or hold something
  • To cause to happen or produce a particular effect

draw

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US / drɔ: /

UK / drɔ /

A1
  • noun
  • Something that attracts people to visit a place
  • A lottery or prize
  • Result of a game, contest where the score is equal
  • verb
  • To attract attention to someone or something
  • To get closer to or approach something or someone
  • To influence a person's involvement in something
  • To move an object by pulling
  • To create an image using pen or pencil and paper
  • To take one thing out of a container, etc.
  • (Of 2 teams) to finish a game with the same score

with

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US / wɪð /

UK / wɪð, wɪθ /

A1
  • preposition
  • As an employee of a certain company
  • Against something or someone
  • By using something as a means
  • Due to; because of
  • Including
  • Possessing as a feature
  • Related to
  • (Of the manner/attitude by which you do something)
  • Used to express that people or things are together

next

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US / nekst /

UK / nɛkst /

A1
  • adverb
  • The one that follows another in time or order
  • At a time or place directly after the present one
  • noun
  • The one that follows after
  • adjecitve
  • Immediately after the previous one
  • First occurrence after the present one

clear

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US / klɪə(r) /

UK / klɪr /

A1
  • adjecitve
  • Empty; without anything in it or on it
  • Being certain and without doubt
  • Being without any streaks, spots, or cracks
  • Easy to understand; well-explained; obvious
  • adverb
  • Completely; entirely; through the whole of
  • Away from; free from
  • verb
  • To recover from or remove a problem
  • To get rid of the entire contents of
  • To give permission for something to happen
  • To make a place or surface empty by removing
  • To prove that someone is not guilty or to blame

line

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US / laɪn /

UK / laɪn /

A1
  • noun
  • Border that divides two places or regions
  • Long crease in the skin, often from age
  • Mark that is long, straight and very thin
  • Row of words, letters or numbers that are written
  • Telephone connection
  • People waiting one behind the other; queue
  • Long thin wire, e.g. for electrical signal
  • verb
  • To put material along the inside of something

talk

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US / tɔ:k /

UK / tɔk /

A1
  • noun
  • Style of speaking
  • Discussion between two countries
  • Giving information in front of people; lecture
  • Saying things or ideas to someone with words
  • verb
  • To make a formal speech about something
  • To say things or ideas to someone with words

graph

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US / græf /

UK / ɡræf /

A2
  • noun
  • Image expressing numerical data in lines or shapes
  • verb
  • To show data using images

equation

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US / ɪˈkweɪʒn /

UK / ɪˈkweʒən, -ʃən /

B1
  • noun
  • Mathematical statement showing things to be equal
  • Complex set of different facts, ideas or issues

question

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US / 'kwestʃən /

UK / ˈkwɛstʃən /

A1
  • noun
  • Issue or problems you are dealing with
  • What you ask about; issue
  • verb
  • To ask for or try to get information
  • To have or express concerns or uncertainty

positive

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US / ˈpɒzətɪv /

UK / ˈpɑzɪtɪv /

A2
  • adjecitve
  • Showing agreement or support for something
  • Being sure about something; knowing the truth
  • Having the charge produced by electrons
  • Being good or useful
  • Showing that a chemical is present in a test

hyperbola

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US / haɪˈpɜːbələ /

UK / haɪˈpɜːrbələ /

A1
  • noun
  • Open curve formed by a plane that cuts the base of a right circular cone

slope

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US / sləʊp /

UK / sloʊp /

B1
  • noun
  • Angle of a decline, e.g. where a road dips down
  • Surface on which people can ski
  • verb
  • To have one end that is not as high as the other

ask

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US / ɑ:sk /

UK / æsk /

A1
  • verb
  • To say to someone that you want something

lower

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US / 'ləʊə(r) /

UK / ˈlaʊɚ, laʊr /

A2
  • adjecitve
  • In a position more near the bottom
  • verb
  • To move something downward to the ground

well

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US / wel /

UK / wɛl /

A1
  • adjecitve
  • Being in a fortunate, good condition or state
  • Healthy and in good condition
  • adverb
  • In an acceptable, proper, or successful manner
  • In a complete, total, or full manner
  • A great and considerable degree
  • In a successful way, in a good or satisfactory way
  • exclamation
  • Used to begin or continue a particular statement
  • Used to show you want to start saying something
  • Used to express that you are waiting for a reply
  • You say this to change the topic of a conversation
  • Used to indicate you are making a final remark
  • noun
  • Long deep hole in the ground to get water
  • verb
  • To cause your eyes to fill with tears

anywhere

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US / ˈeniweə(r) /

UK / ˈeniwer /

A1
  • adverb
  • To any extent or degree (often used with not)
  • In, at or to any place
  • other
  • Use to indicate limits or variation

head

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US / hed /

UK / hɛd /

A1
  • noun
  • Counter for the number of cattle
  • Natural mental ability or intelligence
  • Leader or person with the greatest authority
  • Mind; mental ability; mental state
  • Side of a coin with a head on it
  • Top part of your body with eyes and a mouth
  • Starting point of something, e.g. a river
  • verb
  • To hit a ball with your head in a game
  • To be first or at the front or top (e.g. a list)
  • To travel or move toward a particular place; To go in a particular direction
  • To become the leader of something
  • To lead or be responsible for something

period

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US / ˈpɪəriəd /

UK / ˈpɪriəd /

A1
  • noun
  • Set amount of time during which events take place
  • A way to emphasize what you will say
  • A full stop (.), marking the end of a sentence
  • A menstrual cycle
  • A set time for a class to be held

conic

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US / ˈkɒnɪk /

UK / ˈkɑ:nɪk /

A1
  • other
  • Relating to or resembling a cone

anything

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US / ˈeniθɪŋ /

UK / ˈɛniˌθɪŋ /

A1
  • pronoun
  • A thing of any kind

from

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US / frəm /

UK / frʌm, frɑm,frəm /

A1
  • preposition
  • Starting at a particular place, time or level

minus

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US / ˈmaɪnəs /

UK / ˈmaɪnəs /

A2
  • adjecitve
  • Being close to the bottom of a letter grade
  • noun
  • Negative quality; disadvantage
  • Sign that indicates subtraction
  • preposition
  • Being less than zero in number
  • Used when subtracting one number from another
  • verb
  • To take one number away from another; subtract

out

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US / aʊt /

UK / aʊt /

A1
  • adverb
  • No longer stylish (e.g. fashion)
  • Away from home, business, or the usual place
  • In a direction/movement away from inside or center
  • noun
  • Act when a batter cannot continue playing
  • verb
  • To tell people a secret

over

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US / 'əʊvə(r) /

UK / ˈovɚ /

A1
  • adverb
  • Finished; no longer happening
  • Towards the ground/away from a standing position
  • noun
  • A set of six consecutive balls bowled in cricket
  • other
  • Finished
  • preposition
  • Showing the relation when a thing is above another
  • On or covering something
  • Above or across something
  • More than you need
  • From one side to the other
  • In the direction of; toward

meet

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US / mi:t /

UK / mit /

A1
  • noun
  • Sporting competition e.g. swimming
  • verb
  • To provide something that is necessary
  • To come together at a certain time or place

leave

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US / li:v /

UK / liv /

A1
  • noun
  • Permission to do something
  • Vacation time; time off work
  • verb
  • To go away from; depart
  • To gift property to someone after you die
  • To allow something to continue happening
  • To let something remain unused or available
  • To let something or someone remain somewhere

where

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US / hwɛə /

UK / hwɛr, wɛr /

A1
  • conjunction
  • At or in the place which
  • In whatever place
  • pronoun
  • Word you use to ask the location of something

asymptote

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US / 'æsɪmptəʊt /

UK / 'æsɪmˌtoʊt /

A1
  • noun
  • Straight line that is the limiting value of a curve; can be considered as tangent at infinity

and

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US / ənd /

UK / ənd, ən,ænd /

A1
  • conjunction
  • Used to refer to two or more things
  • Plus; in addition; on top of that
  • Used to introduce an action that follows another

any

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US / 'enɪ /

UK / ˈɛni /

A1
  • adjecitve
  • One, or some, no matter which
  • pronoun
  • One (thing) of many; some

come

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US / kʌm /

UK / kʌm /

A1
  • verb
  • To arrive at a place
  • (Of mail) to be delivered
  • To move toward someone; go with someone
  • To reach a certain point or state

think

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US / θɪŋk /

UK / θɪŋk /

A1
  • verb
  • To have an idea about something without certainty
  • To have an idea, opinion or belief about something

region

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US / 'ri:dʒən /

UK / ˈridʒən /

A2
  • noun
  • Part of a country, of the world, area, etc.

radius

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US / ˈreɪdiəs /

UK / ˈrediəs /

B2
  • noun
  • Area around a certain point
  • Long bone on the thumb side of your lower arm
  • Line from the center to the edge of a circle

something

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US / ˈsʌmθɪŋ /

UK / ˈsʌmθɪŋ /

A1
  • adverb
  • In some degree or measure
  • noun
  • a person or thing of some value or consequence
  • pronoun
  • Thing that is not yet known or named
  • Approximately

only

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US / ˈəunli /

UK / ˈonli /

A1
  • adverb
  • Just one; just that amount or thing; not more than
  • Not very important or serious
  • Just that type of thing, person
  • Short time ago; not before a certain time
  • conjunction
  • Except; but

about

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US / ə'baʊt /

UK / əˈbaʊt /

A1
  • adverb
  • To be ready to; going to
  • Nearly; approximately; roughly
  • Near; next to; close to
  • In every direction; in the area of
  • preposition
  • Concerning or of (a topic)

like

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US / laɪk /

UK / laɪk /

A1
  • adjecitve
  • Being equal in status or kind to something else
  • Similar; the same
  • adverb
  • For example
  • preposition
  • Used as a filler; used to ad emphasis
  • In a way similar to the way something is done
  • Such as; for example
  • verb
  • To want to
  • To find something pleasing; to prefer something

that

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US / ðæt /

UK / ðæt, ðət /

A1
  • adjecitve
  • The person or thing being talked about
  • Used to identify something both the speakers know
  • adverb
  • Used to reinforce adjectives and adverbs
  • To such a degree
  • conjunction
  • Used to connect a noun clause
  • Used to introduce an adverbial clause
  • Used to introduce a noun clause
  • determiner
  • Used as a noun to refer to something
  • pronoun
  • Referring an object far away
  • Used to refer to the relative pronoun ‘which’

what

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US / wɒt /

UK / hwɑt, hwʌt, wɔt, wʌt,hwət, wət /

A1
  • pronoun
  • Thing or things that; the same kind as
  • Used to emphasize something you are about to say
  • adjecitve
  • Used to refer to a particular amount, or number
  • Used to place emphasis on a particular quality
  • adverb
  • To a certain degree
  • determiner
  • Question words used for asking for information
  • exclamation
  • Used to express excitement, shock, or surprise
  • Used to ask people to repeat something they said

right

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US / raɪt /

UK / raɪt /

A1
  • adjecitve
  • Correct or true
  • The south side of you looking at the rising sun
  • adverb
  • Exactly in a place or time
  • Being appropriate for a particular event
  • In a straight or direct manner
  • noun
  • Something you are legally or morally allowed to do
  • Ideal of what is just and good
  • Political view based on conservatism
  • verb
  • To fix something previously wrong or unjust
  • To make upright, as a boat that has turned over

bunch

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US / bʌntʃ /

UK / bʌntʃ /

B1
  • noun
  • A group of things of the same kind
  • verb
  • To group people or things closely together
  • (Cloth) to gather/be gathered together in folds

catch

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US / kætʃ /

UK / kætʃ, kɛtʃ /

A1
  • noun
  • Amount of something that has been caught
  • Trick or something trying to deceive
  • verb
  • To stop something flying and hold it
  • To stop something and not let it go, e.g. animals
  • To get sick or get a disease from someone else
  • To find someone to do something, a task
  • To get stuck on or in something
  • To be trapped so you can’t escape
  • To be able to understand what someone is saying

square

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US / skweə(r) /

UK / skwɛr /

A2
  • adjecitve
  • Being fair or honest
  • Multiply a number by itself e.g. 2x2 or 6x6
  • noun
  • Shape with 4 equal length sides and 4 equal angles
  • The result of multiplying Length by the width
  • Open public area in the middle of the town
  • verb
  • To make something balance or be equal
  • To multiply a number by itself, e.g. 2x2 or 6x8
  • To straighten the edge to form a four-sided shape

first

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US / fɜ:st /

UK / fɚst /

A1
  • adjecitve
  • 1st; Coming before all others in time or place
  • noun
  • Something that has not happened before
  • Position of the winner of a competition

get

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US / ɡet /

UK / ɡɛt /

A1
  • verb
  • To become affected by illness or disease
  • To begin to feel or understand an emotion or idea
  • To send or bring someone or something home, etc.
  • To go somewhere to obtain something
  • To (cause to) do a particular thing
  • To obtain, receive or be given something
  • To currently have
  • To prepare for use
  • To understand something being said or read

down

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US / daʊn /

UK / daʊn /

A1
  • adjecitve
  • Being sad, sick, or unhappy
  • Not operating, working, or functioning as expected
  • adverb
  • In a sitting or lying position
  • Towards or on the ground, floor, or bottom
  • Written or copied onto a piece of paper or book
  • noun
  • A period of play in American Football
  • The soft, smooth hairs that cover a bird's body
  • preposition
  • Along something's path, course, or direction
  • Going from a higher position to a lower position
  • verb
  • To eat or drink very quickly and without stopping

must

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US / məst /

UK / mʌst /

A1
  • noun
  • Something that is necessary or required
  • other
  • (Used to state that something ought to be true)
  • Used to say something is required or necessary

slowly

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US / ˈsləʊli /

UK / ˈsloʊli /

A1
  • adverb
  • In an unhurried or not speedy manner

then

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US / ðen /

UK / ðɛn /

A1
  • adverb
  • A time that is not now
  • Following another thing in time or arrangement
  • Following on reasonably from what was just stated
  • At that time, not now

find

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US / faɪnd /

UK / faɪnd /

A1
  • noun
  • Object discovered by chance
  • Things that have been discovered from searching
  • verb
  • To become aware of something that is happening
  • To discover or meet by chance
  • To decide if someone is guilty of a crime, or not
  • To learn through study, research, or effort
  • To discover something by looking for it

bottom

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US / 'bɒtəm /

UK / ˈbɑtəm /

A2
  • adjecitve
  • Concerning the part under something, e.g. a vase
  • noun
  • The part of your body you sit on
  • Lowest position, often in a company or contest
  • Lowest part of something; part on which it rests
  • Lowest level, part or point of an object
  • The part under something, e.g. a vase
  • verb
  • To hit the lowest part of something

happen

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US / 'hæpən /

UK / ˈhæpən /

A1
  • verb
  • To take place or occur

axis

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US / ˈæksɪs /

UK / ˈæksɪs /

B1
  • noun
  • A line about which a rotating body turns

always

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US / 'ɔ:lweɪz /

UK / ˈɔlwez,-wɪz,-wiz /

A1
  • adverb
  • For a very long time
  • At all times; in every situation
  • For ever

describe

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US / dɪ'skraɪb /

UK / dɪˈskraɪb /

A1
  • verb
  • To tell the appearance, sound, smell of something

will

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US / wɪl /

UK / wɪl /

A1
  • noun
  • Desire or choice of someone
  • Document saying who gets your money when you die
  • Strong desire to do something; determination
  • Desire to do something; strong wish to do
  • other
  • Used with verbs to express the future
  • verb
  • To leave property to someone after your death
  • To use mental effort to make something happen
  • Am (is, are) likely to do
  • To influence someone to do something
  • To make something happen by strongly wanting it

point

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US / pɔɪnt /

UK / pɔɪnt /

A1
  • noun
  • An item to be discussed
  • Small spot or dot
  • Fact or detail
  • Feature of something
  • The size of the text on a page or screen
  • A certain time or stage in a process
  • Certain position in time or space
  • Idea or fact you try to convince people about
  • Measurement of scores in a game, sport
  • Sharp end of something, e.g. a pen or pin
  • verb
  • To face a certain direction, e.g. north
  • To indicate something with your finger to others

intersect

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US / ˌɪntə'sekt /

UK / ˌɪntɚˈsɛkt /

B2
  • verb
  • To divide something by crossing it

plus

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US / plʌs /

UK / plʌs /

A2
  • noun
  • A benefit or advantage
  • preposition
  • In addition; add
  • In addition to; Indicates a number above
  • Having a value greater than zero

side

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US / saɪd /

UK / saɪd /

A1
  • adjecitve
  • In addition to the central or most important thing
  • Next to, or very close to, the right or left of
  • noun
  • Position or opinion that is opposite to another
  • Right or left part of a person's body
  • Feature of someone's personality
  • Straight edge of an object
  • One of two or more groups fighting each other
  • verb
  • To decide to agree with one point, not the other

somehow

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US / ˈsʌmhaʊ /

UK / ˈsʌmˌhaʊ /

A1
  • adverb
  • In a way that is not known or certain

here

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US / hɪə(r) /

UK / hɪr /

A1
  • adverb
  • In this place; at this location, position or time

try

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US / traɪ /

UK / traɪ /

A1
  • noun
  • Act of putting the ball over the rugby goal line
  • verb
  • To make an effort, to attempt to do something
  • To examine someone or something in a court of law
  • To test to see if it is good or you like it
  • To make a person go through hardship; test
  • To examine something to see if it works

actually

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US / ˈæktʃuəli /

UK / ˈæktʃuəli /

A1
  • adverb
  • Used to add new (often different) information

realize

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US / 'ri:əlaɪz /

UK / ˈriəˌlaɪz /

A1
  • verb
  • To become aware of or understand mentally

write

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US / raɪt /

UK / raɪt /

A1
  • verb
  • To compose letters and words on paper or a screen
  • To invent or create a computer program
  • To create a song or piece of music

probably

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US / ˈprɒbəbli /

UK / ˈprɑbəbli /

A1
  • adverb
  • That is likely to happen or be true

feeling

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US / ˈfi:lɪŋ /

UK / ˈfilɪŋ /

A1
  • noun
  • Sensation or emotion you experience
  • verb
  • To be aware of or experience an emotion, sensation
  • To sense through direct contact; touch

same

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US / seɪm /

UK / sem /

A1
  • adjecitve
  • Being equal in quality and amount
  • Identical; not different
  • Not changing; constant

can

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US / kæn /

UK / kən,kæn /

A1
  • noun
  • A metal container for storing food
  • other
  • Able to; have the skill to; have the time to
  • verb
  • To have permission to
  • To be possible to do
  • To preserve food by sealing it in a metal container

towards

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US / tə'wɔ:dz /

UK / 'təuədz, twɔ:dz /

A1
  • preposition
  • In the direction of someone or something

horizontal

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US / ˌhɒrɪˈzɒntl /

UK / ˌhɔ:rəˈzɑ:ntl /

B1
  • adjecitve
  • Concerning the horizon
  • A level and flat position

want

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US / wɔnt /

UK / wɑnt, wɔnt /

A1
  • noun
  • Something you desire or wish for
  • State or condition of poverty
  • verb
  • To desire or wish for something; hope for a thing

video

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US / 'vɪdɪəʊ /

UK / ˈvɪdiˌo /

A2
  • adjecitve
  • Of a moving film, with sound
  • noun
  • Recording capturing action with sound
  • verb
  • To make a moving film of, with sound

definition

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US / ˌdefɪˈnɪʃn /

UK / ˌdɛfəˈnɪʃən /

A2
  • noun
  • Explanation of word's meaning, as in dictionaries
  • The sharpness of an image on a screen
  • Visual clearness in a photo or on a screen

equal

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US / 'i:kwəl /

UK / ˈikwəl /

A1
  • adjecitve
  • Same in shape, size, or number
  • verb
  • To add up or be the same as

now

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US / naʊ /

UK / naʊ /

A1
  • adverb
  • At the present time or moment
  • Right away or in the next possible moment
  • Used to refer to something that just happened
  • Time between the present and a moment in the past
  • conjunction
  • Resulting from or because of something

visualize

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US / ˈvɪʒuəlaɪz /

UK / ˈvɪʒuəˌlaɪz /

B1
  • verb
  • To create a picture in your mind of something

maybe

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US / ˈmeɪbi /

UK / ˈmebi /

A1
  • adverb
  • Possibly but not certainly; perhaps

our

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US / 'aʊə(r) /

UK / aʊr /

A1
  • determiner
  • Belonging to us

not

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US / nɒt /

UK / nɑt /

A1
  • adverb
  • Word indicating the negative
  • (Used to form the negative of verbs)

whole

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US / həul /

UK / hol /

A1
  • adjecitve
  • Complete or full; all of
  • Being in a good condition
  • noun
  • Complete amount or sum; total

blue

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US / blu: /

UK / blu /

A1
  • adjecitve
  • Color of the clear sky
  • Feeling sad or down

would

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US / wʊd /

UK / wʊd /

A1
  • other
  • Used to indicate something imagined
  • Used to ask or request something politely
  • Verb used to indicate possibility, request etc.
  • Used to indicate a preference
  • Used to indicate a reaction
  • Indicates something that occurred repeatedly
  • Used to indicate willingness or ability to do

but

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US / bət /

UK / bʌt,bət /

A1
  • conjunction
  • Used before you say something different, opposite

especially

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US / ɪˈspeʃəli /

UK / ɛˈspɛʃəli, ɪˈspɛʃ- /

A1
  • adverb
  • More than usual; extremely
  • Subtitles section
  • The circle x squared plus y squared minus 8x equals 0, and the hyperbola x squared over 9 minus y squared over 4 equal 1 intersect at the points A and B. Equation of a common tangent with positive slope to the circle as well so the hyperbola is-- so let's just visualize what they're asking first.
  • And this is going to take us multiple videos, I have a feeling.
  • But let's just visualize it just so we can get our head around the problem.
  • So this circle, let me complete the square in terms of x.
  • So this circle, as they wrote it, is x squared minus 8x.
  • And then we have a plus y squared-- I left some space here so we can complete the square-- is equal to 0.
  • And then let me add half of this 8 term squared to both sides.
  • So half of negative 8 is negative 4, and negative 4 squared is 16.
  • So add 16 to both sides.
  • And that allowed me to turn the x-term into a perfect square.
  • This is the same thing as x minus 4 squared.
  • And then we have plus y squared.
  • Plus y squared is equal to 16.
  • So this is a circle.
  • This right here is a circle with center at x equals 4.
  • At x equals 4, y is equal to 0.
  • And it has a radius of 4 as well.
  • So let me graph this circle here.
  • So let me draw the horizontal axis, my x-axis.
  • Let me draw the y-axis.
  • That is my y-axis over here.
  • And let me draw its center, so 1, 2, 3, 4.
  • 4 comma 0.
  • That's it's center, and it has a radius of 4.
  • So it's going to come out, and it's going to look something-- I could draw a better circle than that.
  • It's going to look something like-- that's the top half, and then the bottom half is going to look something like that.
  • So that's our circle.
  • Now let's think about the hyperbola.
  • So if we just look at it, the x squared term is positive, so it's going to be a hyperbola that opens to the right and the left.
  • We do this a bunch in the conic sections videos if you want to review of that.
  • And we could just figure out where it intersects the x-axis.
  • So then when y is equal to 0, we have x squared over 9 must be equal to 1.
  • Or x would be plus or minus 3.
  • So the hyperbola is going to look like this.
  • So this is at plus 3 comma 0.
  • The hyperbola will open up like that.
  • And then at 1, 2, 3, negative 3 comma 0, the hyperbola is going to open up to the left.
  • And so in the problem when they describe the points A and B, they're probably talking about that point A and that point B.
  • Now, let's think about what this question is asking us.
  • Equation of a common tangent with positive slope-- so it has to have a positive slope-- to the circle as well as to the hyperbola-- a common tangent.
  • So let's just think about this a little bit.
  • So it's going to have a positive slope, so it won't be tangent to the circle anywhere where the circle has a negative slope.
  • So it can't be tangent over here.
  • It can't be tangent over there.
  • And then we could say, well, if it was tangent to the circle over here, what would happen?
  • Well , it wouldn't be able to be tangent to the hyperbola.
  • So it has to be tangent to the circle someplace in this blue region right over here.
  • And then how can it be tangent to the hyperbola?
  • It might be tempting to say that it would be tangent to the hyperbola in this way somehow, but what you need to realize is the hyperbola is asymptoting towards some line.
  • And we could figure out what that line is.
  • Its asymptoting towards some line.
  • So let me draw that line.
  • The hyperbola is always going to have a higher slope than that line, a very slightly higher slope.
  • It's slowly approaching that line.
  • So if you go out here, the hyperbola is going to have a higher slope than the asymptote line.
  • And so if you had to be tangent to it, you would have to have a higher slope.
  • And anything that's coming from this part of the circle towards anything out here on the hyperbola is going to have to have a lower slope than the tangent line, right?
  • Because it's going to have to catch up.
  • The tangent line is going to have to catch up to whatever-- let me draw it again-- to whatever we draw over here.
  • I want to make this clear.
  • The hyperbola, as you go out here, actually this whole period, this whole part of the hyperbola, is going to have a higher slope than what it is asymptoting towards.
  • That's what allows it to get closer and closer to that line.
  • So any tangent is going to have to have a higher slope out here.
  • Anything tangent to the hyperbola is going to have to have a higher slope than this actual line.
  • It's going to have to have a slightly higher slope.
  • So if we take something out here and we try to draw a tangent from this part of the circle out there, it wouldn't work.
  • Because this tangent, by definition, in order to meet the hyperbola, is going to have to have a lower slope than this asymptote.
  • So this can't be tangent to that part of the hyperbola.
  • So what else can we do?
  • Well, the only other part of the hyperbola that we might be able to work something out is this part of the hyperbola right over here.
  • So if we find a line that's tangent maybe there and there on the hyperbola, then we might have found our common tangent with positive slope.
  • So let me draw that.
  • So our common tangent with positive slope, I'll do that in pink.
  • Our common tangent with positive slope could look like that.
  • So now that we have the visualization down, in the next video let's try to figure out what that line might look like, especially when we constrain it to having to be tangent to the circle and having to be tangent to this hyperbola.