Two Ellipses Sharing a Focus

Difficulty: Medium · Topics: Geometry, Conic Sections, Ellipse

Umumiy fokusli ikki ellips

Two ellipses C 1 and C 2 share the focus F and have major axes of length 12 and 18 respectively. They meet at two distinct points P and Q. Let F 1 and F 2 be the remaining focus of C 1 and of C 2.

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What is the difference between the perimeter of triangle PQF 1 and the perimeter of triangle PQF 2? (The three points F, F 1, F 2 lie on one line.)