A Locus from Perpendicular Focal Chords

★ 8/10Pole and Polar Substitution conic sections analytic geometry

Problem

Consider the ellipse $\dfrac{x^2}4+\dfrac{y^2}3=1$ with foci $F_1$ , $F_2$ . Perpendicular lines $l_1$ and $l_2$ through $F_1$ and $F_2$ meet the ellipse at $A,B$ and $C,D$ respectively. The lines $AC$ and $BD$ meet at a point $P$ . Find the equation of the locus of $P$ .

Answer

Solution

Difficulty	8/10
Topics	Pole and Polar, Substitution, conic sections, analytic geometry

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