Classification of conics and Cassini curves in Minkowski space-time plane

In this paper we use the Apollonius definition of conics to generate algebraic curves in the Minkowski space-time plane M2, which turn out to be different from classical conic sections. We extend and classify this sort of “M-conics”. We discuss the cases of the singularity points of these M-conics, coming from the transition from timelike world to spacelike world through the lightlike one. Finally, we translate the classical concept of Cassini curves with two foci and that of (multifocal) Cassini curves to Minkowski planes M2.