SOLUTION: find the equation of the hyperbola *asymptotes y=3/2x and y=-3/2x passing through (4, √117)

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Question 644424: find the equation of the hyperbola
*asymptotes y=3/2x and y=-3/2x passing through (4, √117)
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
find the equation of the hyperbola
*asymptotes y=3/2x and y=-3/2x passing through (4, √117)
**
Given asymptotes show center of hyperbola at (0,0)
Since given point is above positive slope line of asymptote, hyperbola has a vertical transverse axis
Standard form of hyperbola with vertical transverse axis: %28y-k%29%5E2%2Fa%5E2-%28x-h%29%5E2%2Fb%5E2=1, (h,k)=(x,y) coordinates of center, which is (0,0) in this case
slopes of asymptotes with vertical transverse axis=±a/b=±3/2
b=2a/3
equation:y%5E2%2Fa%5E2-x%5E2%2Fb%5E2=1
y%5E2%2Fa%5E2-x%5E2%2F%284a%5E2%2F9%29=1
Using coordinates of given point(4,√117)
117%2Fa%5E2-9%2A16%2F4a%5E2=1
117%2Fa%5E2-144%2F4a%5E2=1
117%2Fa%5E2-36%2Fa%5E2=1
81/a^2=1
a^2=81
a=9
b=2a/3=6
b^2=36
equation:y%5E2%2F81-x%5E2%2F36=1