Catacaustics Resultants and Kissing Conics - Greg Egan

"A parabolic mirror will focus light rays arriving parallel to the mirror's axis onto a single point: the focus of the mirror. But what happens more generally when light rays strike curved mirrors with other shapes? If we confine ourselves to two dimensions, we can idealise the mirror as a curve in the plane, and plot out the reflected rays produced by light from a given source. In general, rather than passing through a single point, this family of reflected rays will have a curved “envelope” known as the catacaustic of the mirror curve." 5 out of 5 http://www.gregegan.net/SCIENCE/Catacaustics/Catacaustics.html