解题方法
1 . 如图,已知椭圆
的顶点
,
,
,
分别为矩形
的边
的中点,点
分别满足
,
,直线
与直线
的交点为
.
![](https://img.xkw.com/dksih/QBM/2022/1/19/2897725980491776/2900890972012544/STEM/500907ad-9926-44fe-90a2-43de9447d969.png?resizew=233)
(1)证明:点P在椭圆E上;
(2)设直线l与椭圆E相交于M,N两点,
内切圆的圆心为
.若直线
垂直于x轴,证明直线l的斜率为定值,并求出该定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8868e2ba4401d727f1bcb1f5483b48f5.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/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e59de2142e70bc43cdbb8e72048fe323.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3c55fb8c9a3610f9afc566f2442f632.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/479b683d86776f89171ed3599077e02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab4d9dd5aa98f68c69ceee35e76ed906.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e467c89dbb003c653458b581a7ca92d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0fdbbaeec2bd1b2e7658eb6f532489.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://img.xkw.com/dksih/QBM/2022/1/19/2897725980491776/2900890972012544/STEM/500907ad-9926-44fe-90a2-43de9447d969.png?resizew=233)
(1)证明:点P在椭圆E上;
(2)设直线l与椭圆E相交于M,N两点,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ed4c4e8edbd179f3fc38a6653f18c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32fb50c66cd2de786b39cb442ec54a16.png)
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2022-01-23更新
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2卷引用:四川省雅安市天立教育集团2023-2024学年高二下学期开学考试数学试题