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)
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Hyperbola has a vertical transverse axis.
Its standard form of equation: {{{(y-k)^2/a^2-(x-h)^2/b^2=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^2/81-x^2/175=1}}}
eccentricity: c/a=16/9
y=(81+81x^2/175)^.5
{{{ graph( 300, 300, -20, 20, -20, 20,(81+81x^2/175)^.5,-(81+81x^2/175)^.5) }}}