This report gives the derivation of equations for the ray trace analysis of an antenna consisting of a parabolic dish with a phased array in front of it. The derivation gives the equations for ray tracing in a form suitable for digital computer use. A number of rays from a plane wavefront can be traced through the antenna system to a feed point on the antenna axis. The rays are straight lines, and specular reflection is assumed at the dish. The phased array returns the reflected rays to the feed point which is assumed to lie between the dish and phased array. The major features provided by the analysis and the computer program are the relative phases and path lengths of the rays from the wavefront to the feed point tabulation and computer plots, the total number of rays, the number obscured by the phased array, the number that arrive at the phased-array plane and lie within the phased array itself, a computer-generated plot of the starting points on the wavefront of the rays used in tracing, a plot of the locations of those rays that arrive at the phased- array plane, and an outline of the phased array.