Show that a set R is a ball

Question

Let $R = [(x,y,z): x^2+y^2-2y+z^2+4z \leq 0]$

show that $R$ is a ball by showing that it is the region inside and on the boundary of a sphere. What is centre and the radius?

Answer 1

Hint: $x^2+y^2-2y+z^2+4z=x^2+(y-1)^2+(z+2)^2-5$.