On the Bicircular Quartic

Abstract

A fundamental theorem of the general bicircular quantic, given by Casey, is the following:-

A bicircular quartic can be generated in four and only four ways as the envelope of a circle which cuts a fixed circle orthogonally and whose centre moves on a fixed central conic. This fixed conic is called a focal conic and the four focal conies corresponding to the four methods of generating the quartic are confocal, their foci being the double foci of the quartic.