SOLUTION: Find the equation for the hyperbola with foci (4,6) and (-8,6) and a transverse axis length of 8

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Question 744294: Find the equation for the hyperbola with foci (4,6) and (-8,6) and a transverse axis length of 8
Answer by lwsshak3(11628) About Me  (Show Source):
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Find the equation for the hyperbola with foci (4,6) and (-8,6) and a transverse axis length of 8
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Given hyperbola has a horizontal transverse axis.
Its standard form of equation: %28x-h%29%5E2%2Fa%5E2-%28y-k%29%5E2%2Fb%5E2=1, (h,k)=(x,y) coordinates of center.
For given hyperbola:
center: (-2, 6)
length of transverse axis=8=2a
a=4
a^2=16
c=6 (distance from center to foci on the transverse axis)
c^2=36
c^2=a^2+b^2
b^2=c^2-a^2=36-16=20
Equation of given hyperbola:
%28%28x%2B2%29%5E2%2F16%29-%28%28y-6%29%5E2%2F20%29=1