Solution: Suppose the coordinate of the moving point is , then according to the distance formula between two points in space, 

Therefore, it can be simplified by using the binomial expansion formula , and we get

.

That is

.

This is the equation of the desired trajectory.

　　Note : Usually we omit the work of verifying that "the coordinates of points not on the surface do not satisfy the equation" in the aforementioned problem, the same below.