Answer
$ r=\tan\theta\sec\theta$
or
$r=\frac{\tan\theta}{\cos\theta}$
Work Step by Step
$y=x^{2}$
Convert it into polar co-ordinates.
$r sin\theta=r^{2}\cos^{2}\theta$
This implies,
$ \sin\theta=r\cos^{2}\theta$
$ r=\frac{\sin\theta}{\cos^{2}\theta}$
Hence, $ r=\frac{\sin\theta}{cos\theta}\times\frac{1}{\cos\theta}=\tan\theta\sec\theta$
or
$r=\frac{\tan\theta}{\cos\theta}$
