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

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Answer 1 · 2017-03-10T16:15:53

$r^2sin^2theta-3rcostheta+tantheta+2=0$

The relation between rectangular coordinates $(x,y)$ and polar coordinates $(r,theta)$ is given by

$x=rcostheta$ , $y=rsintheta$ , $r^2=x^2+y^2$

Hence $y=3x^2-2x-xy^2$ can be written as

$rsintheta=3r^2cos^2theta-2rcostheta-r^3costhetasin^2theta$

or $sintheta=3rcos^2theta-2costheta-r^2costhetasin^2theta$

or $r^2costhetasin^2theta-3rcos^2theta+sintheta+2costheta=0$

or $r^2sin^2theta-3rcostheta+tantheta+2=0$

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