Answer
Radius: $4$ and Center: $C(1,3,-2)$
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 $x^2+y^2+z^2-2x-6y+4z=2$
$(x^2-2x+1)^2+(y^2-6y+9)^2+(z^2+4z+4)=2+1+9+4$
or, $(x-1)^2+(y-3)^2+(z+2)^2=16$
or, $(x-1)^2+(y-3)^2+(z-(-2))^2=16$
On comparing the above equation with the equation (1), we get
Radius $R=\sqrt {16}=4$ and Center: $C(1,3,-2)$
