An Average Property of Parabolas

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

Problem

A line through the fixed point $A(-1, 0)$ meets the parabola $C \colon y^2 = 4x$ at $M$ and $N$ , and $Q$ is a point of the parabola different from $M, N$ . If the line $QM$ always passes through $(1, -1)$ , prove that the line $QN$ also always passes through a fixed point, and find it.

Answer

Solution

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

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