Answer
$x^{2}+y^{2}=\displaystyle \frac{y}{x}$
Work Step by Step
Formulas relating rectangular $(x,y)$ and polar $(r,\theta)$ coordinates:
$ x=r\cos\theta$ and $ y=r\sin\theta$
$r^{2}=x^{2}+y^{2}$ and $\displaystyle \tan\theta=\frac{y}{x}$.
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$ r^{2}=\tan\theta$
substitute both sides using the formulas:
$x^{2}+y^{2}=\displaystyle \frac{y}{x}$
