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Published byMuriel Carter Modified over 5 years ago

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Definition A hyperbola is the set of all points such that the difference of the distance from two given points called foci is constant

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Definition The parts of a hyperbola are: transverse axis

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Definition The parts of a hyperbola are: conjugate axis

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Definition The parts of a hyperbola are: center

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Definition The parts of a hyperbola are: vertices

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Definition The parts of a hyperbola are: foci

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Definition The parts of a hyperbola are: the asymptotes

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Definition The distance from the center to each vertex is a units a The transverse axis is 2 a units long 2a2a

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Definition The distance from the center to the rectangle along the conjugate axis is b units b 2b2b The length of the conjugate axis is 2 b units

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Definition The distance from the center to each focus is c units where c

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Sketch the graph of the hyperbola What are the coordinates of the foci? What are the coordinates of the vertices? What are the equations of the asymptotes?

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How do get the hyperbola into an up-down position? switch x and y identify vertices, foci, asymptotes for:

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Definition where ( h, k ) is the center Standard equations:

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Definition The equations of the asymptotes are: for a hyperbola that opens left & right

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Definition The equations of the asymptotes are: for a hyperbola that opens up & down

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Summary Vertices and foci are always on the transverse axis Distance from the center to each vertex is a units Distance from center to each focus is c units where

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Summary If x term is positive, hyperbola opens left & right If y term is positive, hyperbola opens up & down a 2 is always the positive denominator

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Find the coordinates of the center, foci, and vertices, and the equations of the asymptotes for the graph of : then graph the hyperbola. Hint: re-write in standard form Example

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Solution Center: (-3,2) Foci: (-3±,2) Vertices: (-2,2), (-4,2) Asymptotes:

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Example Find the coordinates of the center, foci, and vertices, and the equations of the asymptotes for the graph of : then graph the hyperbola.

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Solution Center: (-4,2) Foci: (-4,2± ) Vertices: (-4,-1), (-4,5) Asymptotes:

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