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# Find a polar equation of the conic in terms of r with its focus at the pole.

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Find a polar equation of the conic in terms of r with its focus at the pole.

Conic: hyperbola, Vertices: (5,pi/2), (2,pi/2)

What I did is found the center to be (7/2,pi/2), so c=7/2, a=3/2, e=7/2/3/2=7/3

Then the horizontal directrix above the pole

r= (7/3)p/1+7/3sin(theta)

r=7p/3+7sin(pi/2)=1, p=10/7

r-10/3+7sin(theta)

Can someone help with where I went wrong?

May 26, 2021

First of all, find the equation in the $xy$ plane then substitute the $r\sin\theta$ and $r\cos\theta$ eqns