Problem A. 584. (March 2013)
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 April 10, 2013.
7 students sent a solution. 5 points: Di Giovanni Márk, Fehér Zsombor, Herczeg József, Janzer Olivér, Szabó 928 Attila. 4 points: Machó Bónis. 0 point: 1 student.