平面直角坐标系XOY中.A1A2B1B2为椭圆X^2/a^2+Y^2/b^2=1(a>b>0)的四个平面直角坐标系XOY中.A1A2B1B2为椭圆X^2/a^2+Y^2/b^2=1(a>b>0)的四个顶点.F为右焦点.直线A1B1与直线A2B2相交于点T.线段OT与椭圆的焦
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![平面直角坐标系XOY中.A1A2B1B2为椭圆X^2/a^2+Y^2/b^2=1(a>b>0)的四个平面直角坐标系XOY中.A1A2B1B2为椭圆X^2/a^2+Y^2/b^2=1(a>b>0)的四个顶点.F为右焦点.直线A1B1与直线A2B2相交于点T.线段OT与椭圆的焦](/uploads/image/z/8925267-3-7.jpg?t=%E5%B9%B3%E9%9D%A2%E7%9B%B4%E8%A7%92%E5%9D%90%E6%A0%87%E7%B3%BBXOY%E4%B8%AD.A1A2B1B2%E4%B8%BA%E6%A4%AD%E5%9C%86X%5E2%2Fa%5E2%2BY%5E2%2Fb%5E2%3D1%28a%3Eb%3E0%29%E7%9A%84%E5%9B%9B%E4%B8%AA%E5%B9%B3%E9%9D%A2%E7%9B%B4%E8%A7%92%E5%9D%90%E6%A0%87%E7%B3%BBXOY%E4%B8%AD.A1A2B1B2%E4%B8%BA%E6%A4%AD%E5%9C%86X%5E2%EF%BC%8Fa%5E2%2BY%5E2%EF%BC%8Fb%5E2%3D1%EF%BC%88a%EF%BC%9Eb%EF%BC%9E0%EF%BC%89%E7%9A%84%E5%9B%9B%E4%B8%AA%E9%A1%B6%E7%82%B9.F%E4%B8%BA%E5%8F%B3%E7%84%A6%E7%82%B9.%E7%9B%B4%E7%BA%BFA1B1%E4%B8%8E%E7%9B%B4%E7%BA%BFA2B2%E7%9B%B8%E4%BA%A4%E4%BA%8E%E7%82%B9T.%E7%BA%BF%E6%AE%B5OT%E4%B8%8E%E6%A4%AD%E5%9C%86%E7%9A%84%E7%84%A6)
平面直角坐标系XOY中.A1A2B1B2为椭圆X^2/a^2+Y^2/b^2=1(a>b>0)的四个平面直角坐标系XOY中.A1A2B1B2为椭圆X^2/a^2+Y^2/b^2=1(a>b>0)的四个顶点.F为右焦点.直线A1B1与直线A2B2相交于点T.线段OT与椭圆的焦
平面直角坐标系XOY中.A1A2B1B2为椭圆X^2/a^2+Y^2/b^2=1(a>b>0)的四个
平面直角坐标系XOY中.A1A2B1B2为椭圆X^2/a^2+Y^2/b^2=1(a>b>0)的四个顶点.F为右焦点.直线A1B1与直线A2B2相交于点T.线段OT与椭圆的焦点恰为OT的中点.求离心率e.不用导数)
平面直角坐标系XOY中.A1A2B1B2为椭圆X^2/a^2+Y^2/b^2=1(a>b>0)的四个平面直角坐标系XOY中.A1A2B1B2为椭圆X^2/a^2+Y^2/b^2=1(a>b>0)的四个顶点.F为右焦点.直线A1B1与直线A2B2相交于点T.线段OT与椭圆的焦
题目有误:直线A1B1与直线A2B2是平行线怎么能相交?
原题:
A1.B1.A2.B2为椭圆X^2/a+Y^2/b=1的四个顶点,F为右焦点,直线A1B2与直线B1F相交于T,线段OT与椭圆交M,M恰为OT中点,则该椭圆的离心率?
A1(-a,0),A2(a,0),B1(0,b),B2(0,-b),F(c,0)
由直线的截距式有
A1B2:x/(-a)+y/(-b)=1
B1F:x/c+y/b=1
联立解得交点T坐标为
Tx=2ac/(a-c)
Ty=-[(a+c)b]/(a-c)
于是OT的中点M的坐标为
Mx=ac/(a-c)
My=-[(a+c)b]/[2(a-c)]
因M在椭圆上,则
[ac/(a-c)]^2/a^2+{-[(a+c)b]/[2(a-c)]}^2/b^2=1
引入c/a=e,并化简整理得e^2+10e-3=0
解得e=2√7-5
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