A Focal Chord Ratio

Problem

Let $F_1$ and $F_2$ be the left and right foci of the ellipse $\dfrac{x^2}3+\dfrac{y^2}2=1$ . A line through $F_1$ meets the ellipse at two points $A$ and $B$ , with $|AF_2|=|AB|$ and

\overrightarrow{F_1B}=\lambda\,\overrightarrow{AF_1}.

Find all possible values of $\lambda$ .

Answer

Solution

Difficulty	7/10
Topics	conic sections, Casework

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