The Ptolemy-Alhazen problem and quadric surface mirror reflection

We discuss the problem of the reflection of light on spherical and quadric surface mirrors. In the case of spherical mirrors, this problem is known as Alhazen's problem. Among a number of equations that solve the spherical mirror problem, we focus on the equation that uses the reflection property of an ellipse and discuss the relationship between this equation and the catacaustic curve of the unit circle. Moreover, we provide an algebraic equation that solves Alhazen's problem for quadric surface mirrors.