名校
解题方法
1 . 已知平面内的一动点
满足方程
.
(1)求动点P的轨迹C的标准方程;
(2)已知点
,过
的直线交轨迹C于A、B两点,若
,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8701e0cce437edc830438b4fe6277d89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b60f3af2658448f1d78e69ca194a40f.png)
(1)求动点P的轨迹C的标准方程;
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56613cbbcda201eff091984e3290a996.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d054e17d28ec3c190340f2055e93102.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3a7681c38f74e21181bb9de077b0c0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3c07ebcbfacda073208d483c58e8a84.png)
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2 . 平面直角坐标系中,等边
的边长为
,M为BC中点,B,C分别在射线
,
上运动,记M的轨迹为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a1b72379b3b15175d1927dd6b0271c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79301e3963cf05b1ac7c249749420475.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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3 . 已知定点
,圆
:
,过
点的直线
交圆于
、
两点,过
点作直线
交
于
点.
(1)求点
的轨迹方程
;
(2)(i)曲线
上有两个点
、
,直线
和
的斜率之积为1,问是否存在实数
,使得
.
(ii)在(i)的条件下,设
的斜率为
,已知
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35366652793f9994cc34b40d9d9af59a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51cdb9fb7479bf61d313ae5638154915.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/172722d11ea7e01411fa06dbb82f46ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d890981c534f33da83f76eaa6f0726cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fddbb7f29e8672f34941fe70b0a1e45f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)(i)曲线
![](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/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bcdf0a7158778502ccbb49f53430159.png)
(ii)在(i)的条件下,设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c800b4b20df6f2441113a7d15134a95c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29aa828f2bd9a5e63ee58dcaa9d0d336.png)
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名校
4 . 在平面直角坐标系
中,动圆
与圆
:
内切,且与圆
:
外切,记动圆
的圆心的轨迹为
.
(1)求轨迹
的方程;
(2)已知
分别为轨迹
的左、右顶点,点
不与
重合.直线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a461995b90655f5133df6f61c2d09bd.png)
与直线
交于点
,
与
轴交于点
,直线
与直线
的交点为
,若四点
共圆.求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e91f4e726059665d140de82d9b105c81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae5ce71568a10700c5d9e813fa8e6c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(1)求轨迹
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a461995b90655f5133df6f61c2d09bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6f7b16d65f1b2b8bea8cf4a83fde925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3ca78154dab846367fabbe29abed277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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5 . 在平面直角坐标系
中,点
,点
是平面内的动点.若以PF为直径的圆与圆
内切,记点P的轨迹为曲线E.
(1)求E的方程;
(2)设点
,
,
,直线AM,AN分别与曲线E交于点S,T(S,T异于A),
,垂足为H,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46542271c7fa06f33b222424838c9684.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79382ba44ba669b5d43fdd5427adf16c.png)
(1)求E的方程;
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383f12cb70ca55eba4ff012771dbfa9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b10c64cc584dde9a132ab54c6981cce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e59cc6019966ce25e3ad146e992f0c68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c60030f98d7cf695840770c05e63dbd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a31666076b1d37cd2f99afa950da5ab.png)
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2023-12-18更新
|
1753次组卷
|
5卷引用:湖南省长沙市长郡中学2024届高三上学期期末适应性考数学试题
湖南省长沙市长郡中学2024届高三上学期期末适应性考数学试题(已下线)模块一 专题2 《解析几何》单元检测篇 B提升卷重庆市南开中学校2023-2024学年高二下学期阶段测试数学试题广东省广州市2024届高三上学期调研测试数学试题(B)(已下线)专题11椭圆(3个知识点7个拓展2个突破7种题型2个易错点)-【倍速学习法】2023-2024学年高二数学核心知识点与常见题型通关讲解练(人教A版2019选修第一册)
23-24高二上·上海浦东新·期中
6 . 如图,D为圆O:
上一动点,过点D分别作x轴,y轴的垂线,垂足分别为A,B,连接
并延长至点W,使得
,点W的轨迹记为曲线
.
(2)若过点
的两条直线
,
分别交曲线C于M,N两点,且
,求证:直线MN过定点;
(3)若曲线C交y轴正半轴于点S,直线
与曲线C交于不同的两点G,H,直线SH,SG分别交x轴于P,Q两点.请探究:y轴上是否存在点R,使得
?若存在,求出点R坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dea2ae9d515f9ab351ad72306b776ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd32c18b556a282803d81e9a229de012.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15066261aaefa8e7384aeca62213497b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ce08b357f11ef44c3e8207ac574422a.png)
(3)若曲线C交y轴正半轴于点S,直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11abb76da45ffa52b47c3a6b9a03ac7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62a0b95d5ba514e87d8d36a0854b1c5d.png)
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2023-11-13更新
|
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8卷引用:湖南省长沙市雅礼实验中学2023-2024学年高二下学期收心检测数学试题
湖南省长沙市雅礼实验中学2023-2024学年高二下学期收心检测数学试题江西省吉安市第一中学2024届高三“九省联考”考后适应性测试数学试题(一)湖北省荆州市沙市中学2024届高三下学期3月月考数学试题(已下线)微考点6-3 圆锥曲线中的定点定值问题(三大题型)江西省景德镇市乐平中学2023-2024学年高二下学期3月月考数学试题(已下线)专题07 直线与圆、圆锥曲线广东省广州市第六中学2023-2024学年高二下学期3月测验数学试题(已下线)上海市华东师范大学第二附属中学2023-2024学年高二上学期期中数学试题
7 . 在平面直角坐标系中,已知点
,
,点
满足
.记
的轨迹为
.
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb2e58d7f7f5736a2ca43175ac584dae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c593ebdb2f1934a0cb56f8c44f454f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b757f0c42ae5c9a2d6a4b19e5877b27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c593ebdb2f1934a0cb56f8c44f454f8.png)
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2023-11-09更新
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3卷引用:湖南省长沙市部分学校2023-2024学年高二下学期入学暨寒假作业检测联考数学试卷
解题方法
8 . 动点P到两定点A(-4,0)、B(4,0)距离之和为10,则点P的轨迹方程为________ .
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2023-01-31更新
|
661次组卷
|
4卷引用:湖南省长沙市德成学校2023-2024学年高二上学期期末数学试题