Answer
$r=4\sin\theta$
Work Step by Step
$x^{2}+y^{2}=4y$
Putting $x=r\cos\theta$ and $y=r\sin\theta$, we have
$r^{2}\cos^{2}\theta+r^{2}\sin^{2}\theta=4r\sin\theta$
$r^{2}(\cos^{2}\theta+\sin^{2}\theta)=4r\sin\theta$
Recall: $\cos^{2}\theta+\sin^{2}\theta=1$
$\implies r^{2}=4r\sin\theta$
Dividing by $r$ on both sides, we get
$r=4\sin\theta$ which is the required equation.
