Parallel Focal Lines

Problem

Let $F_1, F_2$ be the left and right foci of the hyperbola $C \colon \dfrac{x^2}{2} - \dfrac{y^2}{2} = 1$ . A line $l$ through $T(-3, 0)$ meets the left and right branches of $C$ at $M$ and $N$ respectively, and lines $F_1N$ and $F_2M$ meet at $P$ . If $F_1M \parallel F_2N$ , find $|PF_2| - |PF_1|$ .

Answer

Solution

Difficulty	7/10
Topics	Similar Triangles, conic sections, analytic geometry, Triangle Geometry

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