已知椭圆
的左顶点为
,上顶点为
,
为坐标原点,椭圆上的两点
,
分别在第一,第二象限内,若
与
的面积相等,且
,则椭圆
的离心率为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/093fdad4ecbf29897af965532a367e82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/837ba2ee818c137be47190bae5357f63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c29e963e1871b415c086bc600d16bd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60f8a33ab7b6d46fc6aa88c370e54983.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc2aa0ff6946276e538428b7f7ee5ebc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
22-23高二下·浙江温州·期末 查看更多[2]
更新时间:2023-06-27 18:06:46
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【知识点】 求椭圆的离心率或离心率的取值范围
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|
较易
(0.85)
【推荐1】已知
,
分别是椭圆C:
(
)的左,右焦点,B是C的上顶点,过
的直线交C于P,Q两点,O为坐标原点,
与
的周长比为
,则椭圆的离心率为_________ ;如果
,且
,则
的面积为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec11ff3a07361d2d2ab9de7a194524c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fea5f7430235e65d2c2e6b2ecc46712.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f728b7727369bfe12b6054a9bfa0c546.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb5113f2b7714d73c9dc899821485ebf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb2b96cd4d27c2956452c1cd064d3b31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fea5f7430235e65d2c2e6b2ecc46712.png)
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解题方法
【推荐2】法国数学家加斯帕·蒙日被称为“画法几何创始人”“微分几何之父”.他发现椭圆的两条互相垂直的切线的交点的轨迹是以该椭圆的中心为圆心的圆,这个圆被称为该椭圆的蒙日圆.若椭圆
的蒙日圆为
,则
的离心率为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad8bd7057c0f2247b350f41062285811.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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