Answer
Polar equation: $r^2=4r \sin \theta$
and $r=4 \sin \theta$
Work Step by Step
The conversion of polar coordinates and Cartesian coordinates are described as follows:
1. $r^2=x^2+y^2$ and $r=\sqrt {x^2+y^2}$
2. $\tan \theta =\dfrac{y}{x} \implies \theta =\tan^{-1} (\dfrac{y}{x})$
3. $x=r \cos \theta$ and 4. $y=r \sin \theta$
Now, we have the equivalent Polar equation: $(r \cos \theta)^2+(r \sin \theta-2)^2=4$
This implies that $r^2=4r \sin \theta$
and $r=4 \sin \theta$