How do you convert $y=y^2-2x^2 -4x$ into a polar equation?

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Answer 1 · 2017-06-04T20:20:11

The polar equation is $r=(sintheta+4costheta)/(sin^2theta-2cos^2theta)$

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

$x=rcostheta$

$y=rsintheta$

Our equation is

$y=y^2-2x^2-4x$

$rsintheta=r^2sin^2theta-2r^2cos^2theta-4rcostheta$

Dividing by $r!=0$

$sintheta=rsin^2theta-2rcos^2theta-4costheta$

$r(sin^2theta-2cos^2theta)=sin theta+4costheta$

$r=(sintheta+4costheta)/(sin^2theta-2cos^2theta)$

How do you convert y=y^2-2x^2 -4x y=y^2-2x^2 -4x into a polar equation?