A Ratio of Distances, Minimized

★ 6/10Extrema conic sections analytic geometry

Problem

The distance from the point $M(3, 2)$ to the directrix of the parabola $C \colon y = ax^2$ (with $a > 0$ ) is $4$ . Let $F$ be the focus of the parabola, let $N(1, 1)$ , and let $P$ move along the line $l \colon x - y - 2 = 0$ . Find the minimum value of

\frac{|PN| - 1}{|PF|}.

Answer

Solution

Difficulty	6/10
Topics	Extrema, conic sections, analytic geometry

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