How do you convert $xy=x-2y-3y^2$ into a polar equation?

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Answer 1 · 2017-06-06T06:52:18

The polar equation is $r=(costheta-2sintheta)/(sinthetacostheta+3sin^2theta)$

To convert from rectangular coordinates $(x,y)$ to polar coordinates $(r,theta)$ , we apply the following equations

$x=rcostheta$

$y=rsintheta$

Therefore,

$xy=x-2y-3y^2$

$rcostheta*rsintheta=rcostheta-2rsintheta-3r^2sin^2theta$

$r^2costhetasintheta=rcostheta-2rsintheta-3r^2sin^2theta$

As $r!=0$ , we divide by $r$

$rcosthetasintheta=costheta-2sintheta-3rsin^2theta$

$rsinthetacostheta+3rsin^2theta=costheta-2sintheta$

$r(sinthetacostheta+3sin^2theta)=costheta-2sintheta$

So,

$r=(costheta-2sintheta)/(sinthetacostheta+3sin^2theta)$

How do you convert xy=x-2y-3y^2 xy=x-2y-3y^2 into a polar equation?