Answer
$$r = \tan \theta \sec \theta $$
Work Step by Step
$$\eqalign{
& y = {x^2} \cr
& {\text{Use }}r\sin \theta = y{\text{ and }}r\cos \theta = x,{\text{ then}} \cr
& r\sin \theta = {\left( {r\cos \theta } \right)^2} \cr
& r\sin \theta = {r^2}{\cos ^2}\theta \cr
& \sin \theta = r{\cos ^2}\theta \cr
& {\text{Divide both sides by co}}{{\text{s}}^2}\theta \cr
& \frac{{\sin \theta }}{{{{\cos }^2}\theta }} = r \cr
& r = \left( {\frac{{\sin \theta }}{{\cos \theta }}} \right)\left( {\frac{1}{{\cos \theta }}} \right) \cr
& r = \tan \theta \sec \theta \cr} $$
