MathDB
Hyperbola

Source: 1997 National High School Mathematics League, Exam One, Problem 14

March 4, 2020
conicshyperbola

Problem Statement

Two branches of the hyperbola xy=1xy=1 are C1,C2C_1,C_2 (C1C_1 in Quadrant I, C2C_2 in Quadrant III). Three apexes of regular triangle PQRPQR are on the hyperbola. (a) P,Q,RP,Q,R cannot be on the same branch. (b) P(−1,−1)P(-1,-1) is a point on C2C_2, if Q,RQ,R are on C1C_1, find their coordinates.
Back to ProblemsView on AoPS