A Min Area from Perpendicular Chords

★ 8/10Extrema Parametrization conic sections

Problem

The parabola $y^2=4x$ has focus $F$ . Through $F$ , two perpendicular lines meet the parabola at $A,B$ and $C,D$ respectively. Let $M$ , $N$ be the midpoints of the chords $AB$ , $CD$ , and let the lines $AC$ , $BD$ meet at a point $G$ . Find the minimum area of $\triangle GMN$ .

Answer

Solution

Difficulty	8/10
Topics	Extrema, Parametrization, conic sections

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