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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
Definition The parts of a hyperbola are: transverse axis
Definition The parts of a hyperbola are: conjugate axis
Definition The parts of a hyperbola are: center
Definition The parts of a hyperbola are: vertices
Definition The parts of a hyperbola are: foci
Definition The parts of a hyperbola are: the asymptotes
Definition The distance from the center to each vertex is a units a The transverse axis is 2 a units long 2a2a
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
Definition The distance from the center to each focus is c units where c
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?
How do get the hyperbola into an up-down position? switch x and y identify vertices, foci, asymptotes for:
Definition where ( h, k ) is the center Standard equations:
Definition The equations of the asymptotes are: for a hyperbola that opens left & right
Definition The equations of the asymptotes are: for a hyperbola that opens up & down
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
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
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
Solution Center: (-3,2) Foci: (-3±,2) Vertices: (-2,2), (-4,2) Asymptotes:
Example Find the coordinates of the center, foci, and vertices, and the equations of the asymptotes for the graph of : then graph the hyperbola.
Solution Center: (-4,2) Foci: (-4,2± ) Vertices: (-4,-1), (-4,5) Asymptotes:
What is it?.
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HYPERBOLA. PARTS OF A HYPERBOLA center Focus 2 Focus 1 conjugate axis vertices The dashed lines are asymptotes for the graphs transverse axis.
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