A Locus from Two Chords

★ 8/10Pole and Polar conic sections analytic geometry

Problem

Consider the hyperbola $\dfrac{x^2}{2} - y^2 = 1$ with fixed points $A(-2, 1)$ and $B(2, 1)$ on it. A line through $M(0, -3)$ meets the hyperbola at $C$ and $D$ , and lines $AC$ and $BD$ meet at $P$ . Find the equation of the locus of $P$ .

Answer

Solution

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

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