The locus of is an ellipse with centre at (5/2, 0), major axis of length 5 and vertices at (0, 0) and (5, 0).

There are several ways to see this - the simplest is if you understand the locus definition of an ellipse ..... Alternatively, you can sub z = x + iy, but there are a couple of twists and turns that will catch the unwary.

This gives a geometric picture of the lay of the land - there's only one intersection point.