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Ellipse Problem

Source: 2003 National High School Mathematics League, Exam One, Problem 8

March 16, 2020
conicsellipsegeometry

Problem Statement

F1,F2F_1,F_2 are two focal points of ellipse x29+y24=1\frac{x^2}{9}+\frac{y^2}{4}=1, PP is a point on the ellipse, and ∣PF1∣:∣PF2∣=2:1|PF_1|:|PF_2|=2:1, then the area of △PF1F2\triangle PF_1F_2 is________.
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