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

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Answer 1 · 2017-05-24T16:59:56

$r^2sintheta(costheta+3sintheta)-rcostheta+2=0$

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

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

Hence we can write $xy=x-2-3y^2$ in polar form as

$rcosthetaxxrsintheta=rcostheta-2-3r^2sin^2theta$

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

or $r^2(sinthetacostheta+3sin^2theta)-rcostheta+2=0$

or $r^2sintheta(costheta+3sintheta)-rcostheta+2=0$

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