A Shortest Tangent Chord

★ 6/10functions calculus Absolute Value AM-GM analytic geometry

Problem

In the coordinate plane, let $\Gamma$ be the graph of $y = \dfrac{1}{|x|}$ . Points $P$ and $Q$ on $\Gamma$ are such that $P$ lies in the first quadrant, $Q$ lies in the second quadrant, and the line $PQ$ is tangent to the second-quadrant branch of $\Gamma$ at $Q$ . Find the minimum value of $|PQ|$ .

Answer

Solution

Difficulty	6/10
Topics	functions, calculus, Absolute Value, AM-GM, analytic geometry

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