An Involution Fixed Point

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

Problem

Consider the ellipse $\dfrac{x^2}{4} + y^2 = 1$ and the fixed point $P(4, 0)$ . A line of slope $1$ meets the ellipse at $A$ and $B$ ; lines $PA$ and $PB$ meet the ellipse again at points $C$ and $D$ (distinct from $A, B$ ). Prove that the line $CD$ passes through a fixed point.

Answer

Solution

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

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