已知椭圆
的左、右焦点分别为
,点
,
在
上,且满足
,
,则
的离心率为_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/475a3fdc7b27d5ffa8c864dc478903d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/888465c45bb120ff2aa979006c87eb7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f79e4292aade9d5ed1d7b40e7e766740.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
更新时间:2024-05-27 00:17:16
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解题方法
【推荐1】已知
,
分别为双曲线
的左、右焦点,若过点
与双曲线C的渐近线
垂直的直线分别交渐近线
和双曲线C的左支于点M,E,且
,则C的离心率为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
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【推荐2】已知
中,
为
的中点,
,
,则
的值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3274aac77f61dc25ab33cf0351b3810.png)
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【推荐1】已知椭圆
的左、右焦点分别为
,过点
且斜率为
的直线与
交于
两点.若
,则
的离心率为_____ ;线段
的垂直平分线与
轴交于点
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d398e2747bec7d0d3900a32b34510da.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d398e2747bec7d0d3900a32b34510da.png)
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【推荐2】在生活中,可以利用如下图工具绘制椭圆,按照这个原理,已知O是滑杆上的一个定点,D可以在滑杆上自由移动,线段
,点B,E是AD上两点,E是AD中点,且
,如图,过B作AD的垂线,满足
,则点E所形成的轨迹
的离心率![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1b988dbce5a9198d61842c95e7747d9.png)
________ ;点C所形成的轨迹
的离心率![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71ced3c956c7292540692adf70b41fd4.png)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43bce604c2a5730b5d9d8bd642f4484d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17ad7e0e730caaebab54e28873c38543.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce5256233ba43fccd2732b983d533f08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1b988dbce5a9198d61842c95e7747d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71ced3c956c7292540692adf70b41fd4.png)
![](https://img.xkw.com/dksih/QBM/2022/5/19/2982704523100160/2984378751426560/STEM/9d582248-3990-417c-bcee-918d6e2003fe.png?resizew=518)
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【推荐1】如图,在
中,已知
,其内切圆与AC边相切于点D,且
,延长BA到E,使
,连接CE,设以E,C为焦点且经过点A的椭圆的离心率为
,以E,C为焦点且经过点A的双曲线的离心率为
,则
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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【推荐2】已知椭圆
:
与圆
:
,若在椭圆
上不存在点P,使得由点P所作的圆
的两条切线互相垂直,则椭圆
的离心率的取值范围是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
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