Answer
$$r = 4\sec \theta \tan \theta $$
Work Step by Step
$$\eqalign{
& {x^2} = 4y \cr
& {\text{Convert to polar form, using }}x = r\cos \theta ,{\text{ }}y = r\sin \theta \cr
& {\left( {r\cos \theta } \right)^2} = 4\left( {r\sin \theta } \right) \cr
& {r^2}{\cos ^2}\theta = 4r\sin \theta \cr
& \frac{{{r^2}{{\cos }^2}\theta }}{r} = \frac{{4r\sin \theta }}{r} \cr
& r{\cos ^2}\theta = 4\sin \theta \cr
& r = 4\left( {\frac{{\sin \theta }}{{{{\cos }^2}\theta }}} \right) \cr
& r = 4\sec \theta \tan \theta \cr
& {\text{The graph represents a parabola }} \cr
& {\text{Graph}} \cr} $$
