Focal Chord Ratios

Problem

$F_1$ and $F_2$ are the foci of the ellipse $\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1$ . A line through $F_1$ meets the ellipse at $P$ and $Q$ . Given

|PF_1| = |F_1F_2| \qquad\text{and}\qquad 2|PF_1| = 3|QF_1|,

find the eccentricity of the ellipse.

Answer

Solution

Difficulty	6/10
Topics	Law of Cosines, conic sections

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