MathDB
Analytic Geometry

Source: 2000 National High School Mathematics League, Exam One, Problem 15

March 11, 2020
geometryparallelogramanalytic geometry

Problem Statement

C0:x2+y2=1,C1:x2a2+y2b2(a>b>0)C_0:x^2+y^2=1,C_1:\frac{x^2}{a^2}+\frac{y^2}{b^2}(a>b>0). Find all (a,b)(a,b) such that for any point PP on C1C_1, we can find a parallelogram with an apex PP, and it is externally tangent to C0C_0, inscribed to C1C_1.
Back to ProblemsView on AoPS