Answer
$ r=\tan\theta\sec\theta$
Work Step by Step
Formulas relating rectangulsr $(x,y)$ 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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$y=x^{2} $
Substitute $ r\cos\theta$ and $ r\sin\theta$ for x and y.
$r\sin\theta=(r\cos\theta)^{2}$
$r\sin\theta=r^{2}\cos^{2}\theta\qquad/\div r$
$\sin\theta=r\cos^{2}\theta\qquad/\div\cos^{2}\theta$
$r=\displaystyle \frac{\sin\theta}{\cos^{2}\theta}=\frac{\sin\theta}{\cos\theta}\cdot\frac{1}{\cos\theta}$
$ r=\tan\theta\sec\theta$
