  This is a survey of metric properties of non-Euclidean conics, mainly based
on works of Chasles and Story. A spherical conic is the intersection of the
sphere with a quadratic cone; similarly, a hyperbolic conic is the intersection
of the Beltrami-Cayley-Klein disk with an affine conic. Non-Euclidean conics
have metric properties similar to those of Euclidean conics, and even more due
to the polarity that works here better than in the Euclidean plane.
