Answer
$r = 6 \sin \theta$
Work Step by Step
we know $x = r \cos \theta$ and $y = r \sin \theta$
putting the values in equation we get
$x^2 +y^2 = 6y$
$=> {(r \cos \theta)}^2 + {(r \sin \theta)}^2 =6r \sin \theta$
$=> r^2({ \cos^2 \theta} + {\sin^2 \theta})=6r \sin \theta$
We know $({ \cos^2 \theta} + {\sin^2 \theta}) = 1$
$=> r^2 = 6r \sin \theta$
$=> r = 6 \sin \theta$
Plot of this equation will be circle of radius 3 and center $(0, 3)$
