A vertical light ray coming from infinity is reflected by a primary parabolic mirror M[subscript 1] having focus at F[subscript 1]. At a small distance from F[subscript 1] a secondary mirror M[subscript 2], symmetric with respect to the vertical axis, is placed. One would like to find the analytic equation of the mirror M[subscript 2], so that all rays from infinity, incident on M[subscript 1], could be sent back to the vertex V[subscript 1] of the primary mirror M[subscript 1]. We denote the mirror M[subscript 2] with the name of "zozzaroid", after P Zozzaro, who first proposed the problem. Recalling the famous legend about Dionysius ear, we find that M[subscript 2] has either an elliptic or a hyperbolic profile. (Contains 6 figures.)