Mathematical and Physical Journal
for High Schools
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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.

(5 pont)

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.

Problems in Mathematics of KöMaL, March 2013