How do you convert $y= 3x^2-5x-y^2$ into a polar equation?

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Answer 1 · 2018-03-20T14:22:22

$r=-(sintheta+5costheta)/(sin^2theta-3cos^2theta)$

For this we need the following:
$x=rcostheta$
$y=rsintheta$

$rsintheta=3(rcostheta)^2-5(rcostheta)-(rsintheta)^2$

$rsintheta=3r^2cos^2theta-5rcostheta-r^2sin^2theta$

$rsintheta+r^2sin^2theta=3r^2cos^2theta-5rcostheta$

$sintheta+rsin^2theta=3rcos^2theta-5costheta$

$rsin^2theta-3rcos^2theta=-sintheta-5costheta$

$r=(-sintheta-5costheta)/(sin^2theta-3cos^2theta)=-(sintheta+5costheta)/(sin^2theta-3cos^2theta)$

How do you convert y= 3x^2-5x-y^2 y= 3x^2-5x-y^2 into a polar equation?