Find the equation of the circle with centre $(0,2)$ and radius $2$

The equation of a circle with centre $(h,k)$ and radius $r$ is given by,
$(x-h){}^2+(y-k){}^2=r{}^2$
Here it is given that centre $(h,k)=(0,2)$ and radius $r=2$
Therefore the equation of required circle is,
$(x-0{)}^2+(y-2{)}^2=2^2$ 
$\Rightarrow x{}^2+y{}^2+4-4y=4$
$\Rightarrow x{}^2+y{}^2-4y=0$