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

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Answer 1 · 2017-01-25T14:46:51

$r(sintheta-3costheta)+r^2(sin2theta-sin^2theta)=0$

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

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

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

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

or $r(sintheta-3costheta)+r^2(sin2theta-sin^2theta)=0$
graph{y=3x-2xy-2y^2 [-23.33, 16.67, -8.72, 11.28]}

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