Point vortex motion on the surface of a spheroid is studied. Exact dynamical equations from the corresponding Hamiltonian are constructed by computing the conformal metric which induces a modified stereographic projection. As a concrete example, the motion of point vortices at the same latitude (called the
point vortex ring
) is investigated as an extension of the sphere case. The role of eccentricity to the stability of the rotating motion is analysed. The influence of a pole vortex is also discussed.