A Secant and a Reflection

★ 7/10Reflection conic sections analytic geometry Vieta's Formulas

Problem

Consider the ellipse $\dfrac{x^2}{4} + \dfrac{y^2}{3} = 1$ and the point $P(4, 0)$ . A secant line through $P$ meets the ellipse at $A$ and $B$ ; let $C$ be the reflection of $B$ across the $x$ -axis.

Prove that the line $AC$ passes through a fixed point.

Answer

Solution

Difficulty	7/10
Topics	Reflection, conic sections, analytic geometry, Vieta's Formulas

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