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...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
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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)的四个顶...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](/uploads/image/z/10428575-23-5.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%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...%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%B5)
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...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
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...
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.
是A1B2于B1F相交于T
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...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
设椭圆方程为x^2/a^2+y^2/b^2=1,F(c,0)
对椭圆进行压缩变换,x'=x/a,y'=y/b
椭圆变为单位圆:x'^2+y'^2=1,F->F'(c/a,0)
【书写方便,变换后图形中字母仍沿用原图形字母,除O外都应加'】
延TO交圆O于N
易知直线A1B2斜率为1,TM=MO=ON=1,A1B2=√2
设T(x,y),则TB2=√2x,y=x+1
由割线定理:TB2*TA1=TM*TN
√2x(√2x+√2)=1*3,
x=(√7-1)/2(负值舍去)
y=(√7+1)/2
易知:B1(0,-1)
直线B1T方程:
(y+1)/[(√7+1)/2+1]=(x-0)/[(√7-1)/2-0]
令y=0
x=2√7-5,即F横坐标
即原椭圆的离心率e=c/a=2√7-5