Mobius transformations and ellipses

Adam Coffman, Marc Frantz

article abstract

This expository article considers non-circular ellipses in the Riemann
sphere, and the action of the group of Mobius transformations.  In
particular, we find which Mobius transformations are symmetries of an
ellipse, and which take one ellipse to another.  We also survey some
of the ``special plane curves'' which appear as inversive images of
the ellipse.