#### Answer

$ r= \tan \theta \sec \theta $

#### Work Step by Step

Given $$ y=x^2$$
Since
$ y=r\sin\theta,\ \ x= r\cos\theta,\ \ r^2=x^2+y^2 $, then
\begin{align*}
y&=x^2\\
r\sin \theta&=r^2 \cos^2\theta \\
\sin \theta&=r \cos^2\theta\\
\end{align*}
Hence
$$ r= \tan \theta \sec \theta $$