Question 817425
write equation for hyperbola with verticies (6,8) (6,0) and asymptotoes y=8(x-6)
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Given hyperbola has a vertical transverse axis.
Its standard form of equation: {{{(y-k)^2/a^2-(x-h)^2/b^2=1}}}, (h,k)=(x,y) coordinates of center
For given hyperbola:
center: (6,4)
length of vertices=8=2a
a=4
a^2=16
asymptote:
y=8(x-6)
y=8x-48
slope=8
slopes of hyperbolas wit vertical transverse axis=±a/b
a/b=±8
b=a/±8=4/±8=±1/2
b^2=1/4
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Equation of given hyperbola:
{{{(y-4)^2/16-(x-6)^2/(1/4)=1}}}