A Rectangle's Fourth Vertex

★ 6/10Parametrization conic sections AM-GM analytic geometry

Problem

A line $l$ meets the parabola $y^2 = 4x$ at two points $A$ and $B$ . If the quadrilateral $OAMB$ (where $O$ is the origin) is a rectangle, find the maximum value of the slope of the line $OM$ .

Answer

Solution

Difficulty	6/10
Topics	Parametrization, conic sections, AM-GM, analytic geometry

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