A Tangent-Line Invariant

★ 7/10Pole and Polar conic sections analytic geometry

Problem

Let $P$ be a point on an ellipse $E$ with foci $F_1, F_2$ , and let $d$ be the distance from the center of $E$ to the tangent line of $E$ at $P$ . Prove that

|PF_1| \cdot |PF_2| \cdot d^2

is independent of the choice of $P$ .

Answer

Solution

Difficulty	7/10
Topics	Pole and Polar, conic sections, analytic geometry

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