已知椭圆x^2/a^2+y^2/b^2=1的左顶点为A,上顶点为B,右焦点为F,设AB中点为M,若2MA*MF+BF^2>0,则该椭圆的离心已知椭圆x^2/a^2+y^2/b^2=1的左顶点为A,上顶点为B,右焦点为F,设AB中点为M,若2向量MA*向量MF+向量BF^2
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![已知椭圆x^2/a^2+y^2/b^2=1的左顶点为A,上顶点为B,右焦点为F,设AB中点为M,若2MA*MF+BF^2>0,则该椭圆的离心已知椭圆x^2/a^2+y^2/b^2=1的左顶点为A,上顶点为B,右焦点为F,设AB中点为M,若2向量MA*向量MF+向量BF^2](/uploads/image/z/3813750-54-0.jpg?t=%E5%B7%B2%E7%9F%A5%E6%A4%AD%E5%9C%86x%5E2%2Fa%5E2%2By%5E2%2Fb%5E2%3D1%E7%9A%84%E5%B7%A6%E9%A1%B6%E7%82%B9%E4%B8%BAA%2C%E4%B8%8A%E9%A1%B6%E7%82%B9%E4%B8%BAB%2C%E5%8F%B3%E7%84%A6%E7%82%B9%E4%B8%BAF%2C%E8%AE%BEAB%E4%B8%AD%E7%82%B9%E4%B8%BAM%2C%E8%8B%A52MA%2AMF%2BBF%5E2%3E0%2C%E5%88%99%E8%AF%A5%E6%A4%AD%E5%9C%86%E7%9A%84%E7%A6%BB%E5%BF%83%E5%B7%B2%E7%9F%A5%E6%A4%AD%E5%9C%86x%5E2%2Fa%5E2%2By%5E2%2Fb%5E2%3D1%E7%9A%84%E5%B7%A6%E9%A1%B6%E7%82%B9%E4%B8%BAA%2C%E4%B8%8A%E9%A1%B6%E7%82%B9%E4%B8%BAB%2C%E5%8F%B3%E7%84%A6%E7%82%B9%E4%B8%BAF%2C%E8%AE%BEAB%E4%B8%AD%E7%82%B9%E4%B8%BAM%2C%E8%8B%A52%E5%90%91%E9%87%8FMA%2A%E5%90%91%E9%87%8FMF%2B%E5%90%91%E9%87%8FBF%5E2)
已知椭圆x^2/a^2+y^2/b^2=1的左顶点为A,上顶点为B,右焦点为F,设AB中点为M,若2MA*MF+BF^2>0,则该椭圆的离心已知椭圆x^2/a^2+y^2/b^2=1的左顶点为A,上顶点为B,右焦点为F,设AB中点为M,若2向量MA*向量MF+向量BF^2
已知椭圆x^2/a^2+y^2/b^2=1的左顶点为A,上顶点为B,右焦点为F,设AB中点为M,若2MA*MF+BF^2>0,则该椭圆的离心
已知椭圆x^2/a^2+y^2/b^2=1的左顶点为A,上顶点为B,右焦点为F,设AB中点为M,若2向量MA*向量MF+向量BF^2>=0,则该椭圆的离心率为?
已知椭圆x^2/a^2+y^2/b^2=1的左顶点为A,上顶点为B,右焦点为F,设AB中点为M,若2MA*MF+BF^2>0,则该椭圆的离心已知椭圆x^2/a^2+y^2/b^2=1的左顶点为A,上顶点为B,右焦点为F,设AB中点为M,若2向量MA*向量MF+向量BF^2
与椭圆相关的各点的坐标为A(-a,0),B(0,b),F(c,0),M(-a/2,b/2)
则向量MA=(-a/2,-b/2),向量MF=(c+a/2,-b/2),向量BF=(c,-b)
2向量MA*向量MF=2(-a/2*(c+a/2)+(b/2)^2)=-ac-a^2/2+b^2/4
向量BF^2=c^2+b^2
2向量MA*向量MF+向量BF^2
=-ac-a^2/2+b^2/4+c^2+b^2
=-ac-a^2/2+c^2+5/4*(a^2-c^2)
=-ac+3/4*a^2-c^2/4
=a^2(-c/a+3/4-1/4*c^2/a^2)
=a^2/4(-4e+3-e^2) (0