Question

关于椭圆的一道选择题椭圆x2/a2+y2/b2=1(a>b>0)的左焦点F到过顶点A(-a,0),B(0,b)的直线的距

Answer 1

过F作FM垂直AB于M，三角形AMF,AOB相似，得

|FM|/|AO|=|AF|/|AB|,即（b/√7)/b=(a-c)/√(a^2+b^2)=√7

7（a-c)^2 = a^2 +b^2 = 2a^2 -c^2

5a^2 -14ac+8c^2 = 0 (5a-4c)(a-2c)=0

a = 4c/5 (椭圆a>c，舍去) a = 2c 所以 e = 1/2