1 . 设动圆
与圆
外切,与圆
内切.
(1)求点
的轨迹
的方程;
(2)过点
且不与
轴垂直的直线
交轨迹
于
,
两点,点
关于
轴的对称点为
,
为
的外心,试探究
是否为定值,若是,求出该定值;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45dfdf970c7611f0d1d8e0e8845d07f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2efa66643cc0df72c29cdde0ff008c6a.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29c040780584f7b30a927f7814f0a7a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9912061b1dcc826a046d588f82f88728.png)
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2023-12-07更新
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1154次组卷
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4卷引用:湖北省十一校2024届高三第一次联考数学试题
2 . 已知两定点P(-1,0),Q(1,0),点M为一个动点,且直线PM,PN的斜率之积为
.
(I)求动点M的轨迹方程,并说明轨迹为一个椭圆;
(Ⅱ)将点M的轨迹上所有点的横坐标、纵坐标分别伸长为原来的
倍,得到一个新的椭圆C,若
为椭圆C的左、右焦点,直线
与椭圆C交于A,B两点,连接
,
并延长交椭圆C于D,E两点,连接DE,证明:AB与DE的斜率之比为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eb5645928b008cffa61b18d36f0263b.png)
(I)求动点M的轨迹方程,并说明轨迹为一个椭圆;
(Ⅱ)将点M的轨迹上所有点的横坐标、纵坐标分别伸长为原来的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30efdb9c7eb4b788352056f3edf21635.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/882651b776851f3f0665de12da6ed47d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8e4e335658db50e46d88f0a17279b1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78aa834961df10c8bc3c64615fb79f05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/983afb4806a678f182659e053a67a77c.png)
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