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

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Answer 1 · 2018-04-13T10:30:32

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

For this we will need:
$x=rcostheta$
$y=rsintheta$

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

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

$sintheta=2rsin^2theta+3rcos^2theta-2rcosthetasintheta$

$sintheta=2rsin^2theta+3rcos^2theta-rsin(2theta)$

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

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

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