MathDB

11

Part of 2011 China Second Round Olympiad

Problems(1)

Ellipse

Source: 0

1/30/2012
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.
conicsellipseanalytic geometrygraphing linesslopegeometryincenter