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.
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![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.](/uploads/image/z/2490699-3-9.jpg?t=%E6%A4%AD%E5%9C%86b%5E2x%5E2%2Ba%5E2y%5E2%3Da%5E2b%5E2%28a%3Eb%3E0%29%E7%9A%84%E5%B7%A6%E7%84%A6%E7%82%B9%E6%98%AFF%2CA%2CB%E6%98%AF%E5%B7%A6%E9%A1%B6%E7%82%B9%E5%92%8C%E4%B8%8A%E9%A1%B6%E7%82%B9%2C%E8%8B%A5F%E5%88%B0%E7%9B%B4%E7%BA%BFAB%E7%9A%84%E8%B7%9D%E7%A6%BB%E6%98%AFb%2F%E6%A0%B9%E5%8F%B77%2C%E6%B1%82%E6%A4%AD%E5%9C%86%E7%9A%84%E7%A6%BB%E5%BF%83%E7%8E%87.)
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)