A. 584. In 3-space, let S be a non-degenerate conic section which is not a circle. Consider the apices of those right circular conical surfaces that contain S. (a) Show that these points lie on a conic section, uniquely determined by S. (b) Denote by C(S) the conic section that contains the possible apices. Prove that C(C(S))=S for arbitrary S.
Deadline expired on 10 April 2013.