SOLUTION: Find the equation of a hyperbola with center (4, 3), vertex (4, 7) and asymptote y-3=4/5(x-4).

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Question 752064: Find the equation of a hyperbola with center
(4, 3), vertex (4, 7) and asymptote y-3=4/5(x-4).
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Find the equation of a hyperbola with center
(4, 3), vertex (4, 7) and asymptote y-3=4/5(x-4).
hyperbola has a vertical transverse axis.
Its standard form of equation: %28y-k%29%5E2%2Fa%5E2-%28x-h%29%5E2%2Fb%5E2=1
a=4 (distance from center to vertex on vertical transverse axis)
a^2=16
slope of asymptote=4/5=a/b
b=5a/4=5
b^2=25
For given hyperbola:
Equation: %28y-3%29%5E2%2F16-%28x-4%29%5E2%2F25=1