双曲线
的右焦点为
,设A、B为双曲线上关于原点对称的两点,
的中点为M,
的中点为N,若原点O在以线段
为直径的圆上,直线
的斜率
,则双曲线的离心率为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5ec7fa23be9cbe9a50607ea6bc8a4ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8db3b46f0bf8897318fb3d0114e56e55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90e0ffff728b43c2a041bc1411744490.png)
更新时间:2021-05-28 20:39:08
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【推荐1】已知双曲线
的焦距为
,且它的渐近线与圆
有交点,连接所有交点的线段围成了几何图形
,则该几何图形
的面积为________ .
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【推荐2】已知双曲线C的中心在坐标原点,一个焦点与抛物线
的焦点相同,且它的一条渐近线方程为
,则C的方程为______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25cb3cc979560a3a2b6cedff82d8acac.png)
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解题方法
【推荐1】已知双曲线
,过点
的直线
与双曲线
在第一象限切于点
,
为双曲线
的右焦点,若直线
的斜率为
,则双曲线
的离心率![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ce2b47812fce4b17fd813d0e4cce21.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2cfa22139b3e9c9a73500e1ba19f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced7dd30b539619dd52366d63f9f4418.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
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解题方法
【推荐2】双曲线
:
的左焦点为
,右顶点为
,过
且垂直于
轴的直线交
的渐近线于点
,
恰为
的角平分线,则
的离心率为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5ec7fa23be9cbe9a50607ea6bc8a4ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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