A Chord Midpoint Height

★ 7/10Extrema conic sections AM-GM analytic geometry

Problem

A chord $AB$ of the parabola $x^2 = 2py$ ( $p > 0$ ) has midpoint $M$ and length $l$ . Find, in terms of $p$ and $l$ , the minimum possible distance $h$ from $M$ to the $x$ -axis.

Answer

Solution

Difficulty	7/10
Topics	Extrema, conic sections, AM-GM, analytic geometry

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