已知
、
是椭圆
的两个焦点,M是椭圆上一点,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/21a9c45d8eb528c4e33308e6fa7f003d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b490e09248ea3242ec67afae8d00c18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08f9a699aededce0ad803bf8257fbbcb.png)
更新时间:2022-03-30 16:50:06
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【知识点】 椭圆中焦点三角形的面积问题
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【推荐1】已知
分别为椭圆
的左、右焦点,P是椭圆上一点.
(1)
的值为________ ;
(2)若
,且
的面积为
,求b的值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4c458c89b04f5a75cc83c528746d4e0.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bfe1cad1ce47339827ac5047af4647d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d124b231bf2cd3746f35e6c68cd7178f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/002ed1ebb2cb936e10ab478789f91c7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92295e0e6d5f7d6743bcb482aabdbe1d.png)
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【推荐2】设椭圆
的左、右焦点分别为
,点
为椭圆
上一动点,则下列说法中正确的是___________
①当点
不在
轴上时,
的周长是6
②当点
不在
轴上时,
面积的最大值为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
③存在点
,使![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2427943a38dcd93c9ec9b735ffc9fe5.png)
④
的取值范围是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/279cefeb5c389a37a71e5fd3925f5954.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
①当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
②当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
③存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2427943a38dcd93c9ec9b735ffc9fe5.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac86e1c253297a377e14fb9a1689be8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da34ce730f711c09909d53806fe2330a.png)
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