Complex numbers (for geometry proof)

What would be a short and straightforward way to prove that

|z-z_1| / |z-z_2| = a

(in which z_1 and z_2 are complex and a is real and independent of z)
implies the existence of a complex number z_0 and a real number R (also
independent of z) so that

|z-z_0| = R

maybe without having to calculate z_0 and R?

.