椭圆b^2x^2+a^2y^2=a^2b^2(a>b>0)的左焦点是F,A,B是左顶点和上顶点,若F到直线AB的距离是b/根号7,求椭圆的离心率.

椭圆b^2x^2+a^2y^2=a^2b^2(a>b>0)的左焦点是F,A,B是左顶点和上顶点,若F到直线AB的距离是b/根号7,求椭圆的离心率.
椭圆b^2x^2+a^2y^2=a^2b^2(a>b>0)的左焦点是F,A,B是左顶点和上顶点,若F到直线AB的距离是b/根号7,求椭圆的离心率.

椭圆b^2x^2+a^2y^2=a^2b^2(a>b>0)的左焦点是F,A,B是左顶点和上顶点,若F到直线AB的距离是b/根号7,求椭圆的离心率.
AB=√(a^2+b^2)
AF=a-c
OB=b
AB:AF=OB:d
√(a^2+b^2):(a-c)=b:(b/√7)
(a^2+b^2):(a-c)^2=7:1
a^2+a^2-c^2=7(a-c)^2
两边同除以a^2得
2-e^2=7(1-e)^2
8e^2-14e+5=0
(2e-1)(4e-5)=0
e=1/2,e=5/4(舍去)