The sphere has it's center at and the constant radius .
2. The two centers are located in the x-y-plane. I've made a sketch of the situation. (see attachment)
3. To get at least points of intersections the two centers must have a distance between 4 and 2. Use Pythagorean theorem to determine the value of c.
Ive got .
4. If the smaller sphere touches the larger sphere from the interior; if the smaller sphere touches the larger sphere from the exterior.
5. If then the points of intersection form a circle.