An Affine Fixed Point

★ 8/10Reflection conic sections analytic geometry Vieta's Formulas

Problem

Consider the ellipse $E \colon \dfrac{x^2}{4} + \dfrac{y^2}{3} = 1$ . A line through $P(2, 1)$ meets the ellipse at $M$ and $N$ ; through $N$ , the line of slope $-\dfrac{3}{2}$ meets the ellipse again at $Q$ . Prove that the line $MQ$ passes through a fixed point.

Answer

Solution

Difficulty	8/10
Topics	Reflection, conic sections, analytic geometry, Vieta's Formulas

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