A Slope Through the Focus

★ 6/10Parametrization conic sections AM-GM analytic geometry Vieta's Formulas

Problem

A parabola $C$ has vertex at the origin $O$ and focus $F$ on the $x$ -axis. A line through the point $(2, 0)$ meets $C$ at two points $P$ and $Q$ with $OP \perp OQ$ , and $M$ is the midpoint of segment $PQ$ . Find the maximum value of the slope of the line $MF$ .

Answer

Solution

Difficulty	6/10
Topics	Parametrization, conic sections, AM-GM, analytic geometry, Vieta's Formulas

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