Answer
Radius $R=\sqrt {8}=2\sqrt 2$ and Center: $C(0,2,2)$
Work Step by Step
The general equation of sphere with center $C(p,q,r)$ and radius $R$ is given by:
$(x-p)^2+(y-q)^2+(z-r)^2=R^2$ ...(1)
Here, we have $x^2+y^2+z^2=4y+4z$
$(x^2-0-0)^2+(y^2-4y+4)^2+(z^2-4z+4)=0+4+4$
or, $(x+0)^2+(y-2)^2+(z-2)^2=8$
or, $(x-(-0))^2+(y-2)^2+(z-2)^2=8$
On comparing the above equation with the equation (1), we get
Radius $R=\sqrt {8}=2\sqrt 2$ and Center: $C(0,2,2)$
