SOLUTION: Write the equation of a hyperbola that passes through the point at (4,2) and has asymptotes with equations y=2x and y=-2x+4.

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Question 113439: Write the equation of a hyperbola that passes through the point at (4,2) and has asymptotes with equations y=2x and y=-2x+4.
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
the center of the hyperbola (h,k) is the intersection of the asymptotes, (1,2)

the parabola passes through (4,2) which is directly above the center
___ this means an East-West opening parabola of the form %28%28%28x-h%29%5E2%29%2Fa%5E2%29-%28%28%28y-k%29%5E2%29%2Fb%5E2%29=1
___ the slope of the asymptotes is ±(b/a), so b=2a and b^2=4a^2

(((4-1)^2)/(a^2))-(((2-2)^2)/(4a^2))=1 ___ ((3^2)/(a^2))-0=1 ___ 3^2=a^2 ___ 3=a ___ so b=6

%28%28%28x-1%29%5E2%29%2F9%29-%28%28%28y-2%29%5E2%29%2F36%29=1