Perpendiculars from a Line

★ 7/10Extrema Circles analytic geometry vectors

Problem

A point $P$ moves along the line $l \colon 2x + y - 2 = 0$ . Two mutually perpendicular lines $PA, PB$ through $P$ meet the $x$ -axis at $A$ and the $y$ -axis at $B$ ; $M$ is the midpoint of $AB$ , and $O$ the origin. Find the minimum value of $\overrightarrow{OM}\cdot\overrightarrow{OP}$ .

Answer

Solution

Difficulty	7/10
Topics	Extrema, Circles, analytic geometry, vectors

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