MathDB
Ellipse

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January 30, 2012
conicsellipseanalytic geometrygraphing linesslopegeometryincenter

Problem Statement

A line ℓ\ell with slope of 13\frac{1}{3} insects the ellipse C:x236+y24=1C:\frac{x^2}{36}+\frac{y^2}{4}=1 at points A,BA,B and the point P(32,2)P\left( 3\sqrt{2} , \sqrt{2}\right) is above the line ℓ\ell.
(1) Prove that the locus of the incenter of triangle PABPAB is a segment,
(2) If ∠APB=π3\angle APB=\frac{\pi}{3}, then find the area of triangle PABPAB.
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