A mirror is to be constructed as a surface of revolution of a certain curve about its symmetry axis such that all incoming rays parallel to the axis will focus at a single point a distance A away from the mirror surface along the axis. Keep in mind that the angle of reflection equals the angle of incidence.
A. Letting y be the symmetry axis, and placing the cocal point at the origin of the (x,y) coordinate system, determine a differential equation for the curve. You should obtain an equation involving (dy/dx)^2.