Find an equation of a sphere with radius r and center C(h, k, ). SOLUTION By definition, a sphere is the set of all points P(x, y, z) whose distance from C is r. (See the figure.) Thus, in terms of r, P is on, the sphere if and only if IPCI- Squaring both sides, in terms of radius r, we have PCI2- In terms of Cartesian coordinates and radius r, the equation of a sphere is +(y k)2 (z - Video Example