椭圆x^2/a^2+y^2/b^2=1,左焦点F1(-c,0),A(-a,0)B(0,b)为2个顶点,F1到直线AB的距离为b/根号7,
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![椭圆x^2/a^2+y^2/b^2=1,左焦点F1(-c,0),A(-a,0)B(0,b)为2个顶点,F1到直线AB的距离为b/根号7,](/uploads/image/z/13220879-23-9.jpg?t=%E6%A4%AD%E5%9C%86x%5E2%2Fa%5E2%2By%5E2%2Fb%5E2%3D1%2C%E5%B7%A6%E7%84%A6%E7%82%B9F1%28-c%2C0%29%2CA%28-a%2C0%29B%280%2Cb%29%E4%B8%BA2%E4%B8%AA%E9%A1%B6%E7%82%B9%2CF1%E5%88%B0%E7%9B%B4%E7%BA%BFAB%E7%9A%84%E8%B7%9D%E7%A6%BB%E4%B8%BAb%2F%E6%A0%B9%E5%8F%B77%2C)
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椭圆x^2/a^2+y^2/b^2=1,左焦点F1(-c,0),A(-a,0)B(0,b)为2个顶点,F1到直线AB的距离为b/根号7,
椭圆x^2/a^2+y^2/b^2=1,左焦点F1(-c,0),A(-a,0)B(0,b)为2个顶点,F1到直线AB的距离为b/根号7,
椭圆x^2/a^2+y^2/b^2=1,左焦点F1(-c,0),A(-a,0)B(0,b)为2个顶点,F1到直线AB的距离为b/根号7,
解析:由题意椭圆的右准线方程可写为:x=a&#178;&#47;c由此可知点E(a&#178;&#47;cbf0)是右准线与x轴的交点在△AF1E中nrvzF1A&#47;&#47;F2B则|F2B|&#47;|F1A|=|EF2|&#47;|EF1|因为|F1A|=2|F2B|fjnr|EF2|=a&#178;&#47;c -c|EF1|=a&#178;&#47;c +c所以(a&#178;&#47;c -c)&#47;(a&#178;&#47;c +c)=1&#47;2即a&#178;&#47;c +c=2(a&#178;&#47;c -c)a&#178;&#47;c =3c则c&#178;&#47;a&#178;=1&#47;3所以椭圆的离心率为e=c&#47;a=√3&#47;3