(1.求椭圆方程(2.过点P(0,2)的直线l与椭圆交于不同的两点A,B,当三角形AOB面积最大时,求IABI的值
F(-c,0), c/a = 1/根号(2)
x^2 / a^2 + y^2 / (a^2 - c^2) = 1
x = -c时, y^2 = (1 - (c/a)^2) a^2 (1-(c/a)^2) = a^2/4, 2y = a = 根号(2)
a^2 = 2, b^2 = 1
x^2/2 + y^2 = 1
如图,OC-AB垂直,D 为AB与x轴交点,设D(d,0),则AB 方程为 x/d + y/2 = 1
A,B 满足 y^2 = 1 - x^2/2, x^2 = (d-dy/2)^2
解得A,B纵坐标分别为:yA = , yB =
S-AOB = 1/2 d (yA-yB) =
解得,S-AOB面积最大值为根号(2)/2,此时AB = 1.5