Question 708598
Find an equation of the hyperbola with the center at the origin. Foci: (0,+-8); asymptotes: y=+-4x.
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FOR SOME UNKNOWN REASON THE COMPLETE SOLUTION WILL NOT POST
Foci data show given hyperbola has a vertical transverse axis.
Standard form of equation: {{{(y-k)^2/a^2-(x-h)^2/b^2=1))), (h,k)=(x,y) coordinates of center
Given slope of asymptotes=±4=a/b
a=±4b
c=8 (distance from center to vertex
c^2=a^2+b^2
8^2=(4b)^2+b^2
64=16b^2+b^2=17b^2
b^2=64/17
b=8/√17
a^2=c^2-b^2=64-(64/17)=1024/17
a=32/√17
Equation:
 {{{y^2/(1024/√17)-x^2/(64/17)=1}}}