若以原点
为圆心的圆同时经过椭圆
的左顶点
及右顶点
,且被过焦点
的直线
分成弧长为
的两段圆弧,则该椭圆的离心率
等于___ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24550b13dbecf7d86c7054250e987274.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ae6b5bbd08a82c75db61627b30a8783.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbe103f073845122c66f22dcb14b711f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
更新时间:2023-11-26 08:16:54
|
【知识点】 求椭圆的离心率或离心率的取值范围
相似题推荐
填空题-单空题
|
适中
(0.65)
解题方法
【推荐1】如图(1),在圆锥内放两个大小不同且不相切的球,使得它们分别与圆锥的侧面、底面相切,用与两球都相切的平面截圆锥的侧面得到截口曲线是椭圆.理由如下:如图(2),若两个球分别与截面相切于点
,在得到的截口曲线上任取一点
,过点
作圆锥母线,分别与两球相切于点
,由球与圆的几何性质,得
,
,所以
,且
,由椭圆定义知截口曲线是椭圆,切点
为焦点.这个结论在圆柱中也适用,如图(3),在一个高为
,底面半径为
的圆柱体内放球,球与圆柱底面及侧面均相切.若一个平面与两个球均相切,则此平面截圆柱所得的截口曲线也为一个椭圆,则该椭圆的离心率为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.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/8bc380e172eb78d4544feedaa016b927.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ee0b63479c3d281efef858a57caff1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ec00cecc8df59ceb54baceff1d68aba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f8a46c01c6f1f24778291300473c546.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08dfcc7ec6874ed5a4362d66f657f719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07ae0b4264da6a8812454ffd2f20d94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://img.xkw.com/dksih/QBM/2020/6/22/2490382251458560/2490841036406784/STEM/dde6ff4ba3164c6eb877c7037f1b38f9.png?resizew=514)
您最近一年使用:0次
填空题-单空题
|
适中
(0.65)
名校
解题方法
【推荐2】已知点F是椭圆
的右焦点,点P在椭圆上,
且
的最小值为3,则椭圆C的离心率是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58ce9b7fd1e231dae339d5beb4181290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a26e951d6d2369e8da79a793a93a66a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44331dd46961efa418e3261d4014b2f7.png)
您最近一年使用:0次