如图,已知椭圆x²/a²+y²/b²=1(a>b>0)的左顶点为A,左焦点为F如图,已知椭圆x²/a²+y²/b²=1(a>b>0)的左顶点为A,左焦点为F,上顶点为B,若∠BAO+∠BFO=90º,求该椭圆的离心
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![如图,已知椭圆x²/a²+y²/b²=1(a>b>0)的左顶点为A,左焦点为F如图,已知椭圆x²/a²+y²/b²=1(a>b>0)的左顶点为A,左焦点为F,上顶点为B,若∠BAO+∠BFO=90º,求该椭圆的离心](/uploads/image/z/3700350-54-0.jpg?t=%E5%A6%82%E5%9B%BE%2C%E5%B7%B2%E7%9F%A5%E6%A4%AD%E5%9C%86x%26%23178%3B%2Fa%26%23178%3B%2By%26%23178%3B%2Fb%26%23178%3B%3D1%EF%BC%88a%3Eb%3E0%29%E7%9A%84%E5%B7%A6%E9%A1%B6%E7%82%B9%E4%B8%BAA%2C%E5%B7%A6%E7%84%A6%E7%82%B9%E4%B8%BAF%E5%A6%82%E5%9B%BE%2C%E5%B7%B2%E7%9F%A5%E6%A4%AD%E5%9C%86x%26%23178%3B%2Fa%26%23178%3B%2By%26%23178%3B%2Fb%26%23178%3B%3D1%EF%BC%88a%26gt%3Bb%26gt%3B0%29%E7%9A%84%E5%B7%A6%E9%A1%B6%E7%82%B9%E4%B8%BAA%2C%E5%B7%A6%E7%84%A6%E7%82%B9%E4%B8%BAF%2C%E4%B8%8A%E9%A1%B6%E7%82%B9%E4%B8%BAB%2C%E8%8B%A5%E2%88%A0BAO%2B%E2%88%A0BFO%3D90%26%23186%3B%2C%E6%B1%82%E8%AF%A5%E6%A4%AD%E5%9C%86%E7%9A%84%E7%A6%BB%E5%BF%83)
如图,已知椭圆x²/a²+y²/b²=1(a>b>0)的左顶点为A,左焦点为F如图,已知椭圆x²/a²+y²/b²=1(a>b>0)的左顶点为A,左焦点为F,上顶点为B,若∠BAO+∠BFO=90º,求该椭圆的离心
如图,已知椭圆x²/a²+y²/b²=1(a>b>0)的左顶点为A,左焦点为F
如图,已知椭圆x²/a²+y²/b²=1(a>b>0)的左顶点为A,左焦点为F,上顶点为B,若∠BAO+∠BFO=90º,求该椭圆的离心率.
如图,已知椭圆x²/a²+y²/b²=1(a>b>0)的左顶点为A,左焦点为F如图,已知椭圆x²/a²+y²/b²=1(a>b>0)的左顶点为A,左焦点为F,上顶点为B,若∠BAO+∠BFO=90º,求该椭圆的离心
作出他的右焦点
所以有三角形ABF'为直角三角形
由射影定理得:BO²=AO*OF'
即在椭圆中a*c=b²再结合 b²=a²-c²可得
a²-c²=a*c
两边同除以ac得
a/c+c/a=1
即 1/e+e=1
可解得 离心率e=(2√5-1)/2 (另一个值舍去,0<e<1)
b/c=a/b e=b2/a2