  We study caustics of an elliptical paraboloid and the history of their
various representations from 3D models in XIX century to the recent computer
graphics. In the paper two ways of generating the surface, one with cartesian
coordinates using formula for principal curvatures, and the other one with
parabolic coordinates using Seidel's formula were demonstrated. By finding the
intersection curves of these caustics with the paraboloid we extend the
solution of F. Caspari for classical Apollonius problem about the number of
concurrent normals to the points of the paraboloid itself. A complete
classification of all possible cases of intersections of these caustics with
their paraboloid is given.
