An Eccentricity Window

★ 7/10Circles conic sections analytic geometry Discriminant

Problem

The ellipse $E \colon \dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1$ has foci $F_1, F_2$ and center $O$ . For a point $P$ on the ellipse, the line through $F_2$ perpendicular to $OP$ meets the segment $F_1P$ at a point $M$ with $F_1M = 2MP$ . Find the range of possible values of the eccentricity $e$ .

Answer

Solution

Difficulty	7/10
Topics	Circles, conic sections, analytic geometry, Discriminant

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