SOLUTION: Find an equation for the hyperbola that satisfies the given conditions. State the coordinate of the center and the eccentricity. Graph. Vertices at (0,+/-9), foci at (0,+/-16)

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Find an equation for the hyperbola that satisfies the given conditions. State the coordinate of the center and the eccentricity. Graph. Vertices at (0,+/-9), foci at (0,+/-16)      Log On


   

Question 972998: Find an equation for the hyperbola that satisfies the given conditions. State the coordinate of the center and the eccentricity. Graph.
Vertices at (0,+/-9), foci at (0,+/-16)
Answer by lwsshak3(11628) About Me  (Show Source):
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Find an equation for the hyperbola that satisfies the given conditions. State the coordinate of the center and the eccentricity. Graph.
Vertices at (0,+/-9), foci at (0,+/-16)
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Hyperbola has a vertical transverse axis.
Its standard form of equation: %28y-k%29%5E2%2Fa%5E2-%28x-h%29%5E2%2Fb%5E2=1, (h,k)=coordinates of center
center: (0, 0)
a=9
a^2=81
c=16
c^2=256
c^2=a^2+b^2
b^2=c^2-a^2=256-81=175
equation: y%5E2%2F81-x%5E2%2F175=1
eccentricity: c/a=16/9
y=(81+81x^2/175)^.5