名校
解题方法
1 . 已知椭圆
的长轴长为4,过点
的直线交椭圆于
两点,
为
中点,连接
并延长交椭圆于点
,记直线
和
的斜率为分别为
和
,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/21/f75b51ed-936b-4ccb-a25a-df32a2ece01d.png?resizew=216)
(1)求椭圆方程;
(2)是否存在点P,使得
为直角?若存在,求
的面积,否则,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ce2d84fae6970174099c616f9e8a1c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef49a3ca580a144cc65a609c167facc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5179a35e8afcbe5eebf7381034206de1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/21/f75b51ed-936b-4ccb-a25a-df32a2ece01d.png?resizew=216)
(1)求椭圆方程;
(2)是否存在点P,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f75f8dbbd0778acd59e16dcb4709f89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e99675fa03da205c4499967c9d908412.png)
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2018-03-04更新
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546次组卷
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2卷引用:江西省吉安市第三中学2024届高三上学期开学考试(艺术类)数学试题