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

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Answer 1 · 2016-05-19T10:43:15

Polar equation is $r=(sintheta-3costheta)/(cos^2theta+2cos2theta)$

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

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

Using them we can convert $y=3x^2+3x-2y^2$ as follows.

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

or $rsintheta=3(rcostheta)^2+3rcostheta-2(rsintheta)^2$

or $rsintheta=3r^2cos^2theta+3rcostheta-2r^2sin^2theta$

or $rsintheta=r^2cos^2theta+3rcostheta+2r^2(cos^2theta-sin^2theta)$

or $sintheta=rcos^2theta+3costheta+2rcos2theta$

or $r=(sintheta-3costheta)/(cos^2theta+2cos2theta)$

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