1 . 如图,已知圆
,圆心是点T,点G是圆T上的动点,点H的坐标为
,线段CH的垂直平分线交线段TC于点R,记动点R的轨迹为曲线E.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/17/7f184f36-d38a-4a16-a68d-696afedbb746.png?resizew=152)
(1)求曲线E的方程;
(2)过点H作一条直线与曲线E相交于A,B两点,与y轴相交于点C,若
,
,试探究
是否为定值?若是,求出该定值;若不是,请说明理由;
(3)过点
作两条直线MP,MQ,分别交曲线E于P,Q两点,使得
.且
,点D为垂足,证明:存在定点F,使得
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7ebdc37c4828abb80c0f3bffb9e54e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5510fbff7fdcc083ef172d4b401c2229.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/17/7f184f36-d38a-4a16-a68d-696afedbb746.png?resizew=152)
(1)求曲线E的方程;
(2)过点H作一条直线与曲线E相交于A,B两点,与y轴相交于点C,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9545ecde4068ea16914263cddb3e8f60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1cff2d267cabb5318d29e319fe65c90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febf7413b35cf2889fdb57a6b519087c.png)
(3)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52b385adf402cd17bddace02fdb32030.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85ebcef3ed51c751de97752bbf40e87c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41b14463c252e686a3cd0a8c4e33c02b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0165236f973be829fd3dbabe9507243.png)
您最近一年使用:0次
2 . 已知⊙C:
(C为圆心)内部一点
与圆周上动点Q连线AQ的中垂线交CQ于M,
(1)求点M的轨迹方程;
(2)若点M的轨迹为曲线X,设
为圆
上任意一点,过
作曲线X的两条切线,切点分别为
,判断
是否为定值?若是,求出定值;若不是,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71e8ffd8a6f46d6076861da6157e8274.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165bd1820c3b3864a20343e15ce2e63.png)
(1)求点M的轨迹方程;
(2)若点M的轨迹为曲线X,设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d35465f3e40ce00a1dce54b943ae183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59880e470359d8e9faf6ae5ce155cf2a.png)
您最近一年使用:0次
3 . 如图,平面
与圆柱相交,而且平面
与圆柱的轴不垂直,点
为平面
与圆柱表面交线上的任意一点,则点
的轨迹
为__________ .在圆柱内部放置两个半径与圆柱底面半径相同的球,平面
分别与两球切于
两点,过点
作圆柱的母线,分别与两球切于
两点,记线段
长度为
,线段
长度为
,且
.在平面
内
的任意两条互相垂直的切线的交点为
,建立适当的坐标系,则动点
的轨迹方程为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eae51f0310b87cde2e206643e9d25a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/23/350088bf-1008-4775-8379-e7c691e5bb56.png?resizew=184)
您最近一年使用:0次
解题方法
4 . 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BA并延长至点W,使得
,点W的轨迹记为曲线C.
(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,并求出定点坐标;
(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/fd32c18b556a282803d81e9a229de012.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)
您最近一年使用:0次
2023-02-10更新
|
732次组卷
|
3卷引用:山东省潍坊市2022-2023学年高二上学期期末考试数学试题
山东省潍坊市2022-2023学年高二上学期期末考试数学试题山东省潍坊市诸城第一中学2022-2023学年高二下学期2月月考数学试题(已下线)湖北省“荆、荆、襄、宜四地七校”考试联盟2023-2024学年高二下学期期中联考数学试卷变式题16-19
名校
解题方法
5 . 如图,已知圆
,动圆P过点
且与圆
内切于点N,记动圆圆心P的轨迹为E.
![](https://img.xkw.com/dksih/QBM/2022/1/17/2896491209203712/2897153509408768/STEM/a977c1a7-866e-4ced-bdbf-a11e275b263e.png?resizew=237)
(1)求E的方程;
(2)过点
的直线l(不与x轴重合)与E交于A,B两点,点C与点B关于x轴对称,直线AC与x轴交于点Q,已知点
,试问
是否为定值?若是,请求出该定值,若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdce30be741dc229f1c6b7fb86b1bb63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc26e1d9bb89a18781de2de48e5aed85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://img.xkw.com/dksih/QBM/2022/1/17/2896491209203712/2897153509408768/STEM/a977c1a7-866e-4ced-bdbf-a11e275b263e.png?resizew=237)
(1)求E的方程;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dfdecc11875b2e969ddc9c5861e1cfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/854390524d8a76983fa263094df4a548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f0423aaabe32062338cfbb250eb08c8.png)
您最近一年使用:0次
2022-01-18更新
|
480次组卷
|
3卷引用:山东省潍坊市2021-2022学年高二上学期期末数学试题
名校
解题方法
6 . 如图,
为椭圆
:
上的动点,过
作椭圆
的切线交圆
:
于
,
,过
,
作
切线交于
,则( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/18/3be06bba-c052-4fd6-957c-84eaa98bd26a.png?resizew=219)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a4c5ff939c836229c3fc0800a1d9fea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58bb8bf0b4bed43989c8c4d158664c3e.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/18/3be06bba-c052-4fd6-957c-84eaa98bd26a.png?resizew=219)
A.![]() ![]() |
B.![]() ![]() |
C.![]() ![]() |
D.![]() ![]() |
您最近一年使用:0次
2021-09-16更新
|
1593次组卷
|
6卷引用:山东省潍坊市昌邑市潍坊实验中学2023-2024学年高二上学期数学期中模拟卷(一)
山东省潍坊市昌邑市潍坊实验中学2023-2024学年高二上学期数学期中模拟卷(一)重庆市名校联盟2021?2022学年高二上学期第一次联合考试数学试题重庆实验外国语学校2022届高三上学期入学考试数学试题(已下线)第十一章 圆锥曲线专练1—椭圆小题1-2022届高三数学一轮复习(已下线)专题9.7 圆锥曲线综合问题 2022年高考数学一轮复习讲练测(新教材新高考)(练)河北省冀东名校2022-2023学年高三上学期期中调研考试数学试题
7 . 如图,已知圆
,点
是圆
内一个定点,
是圆
上任意-一点,线段
的垂直平分线
和半径
相交于点
,连接
,记动点
的轨迹为曲线
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/510cddda-2448-4c58-8e3f-c752f4e7c78e.png?resizew=175)
(1)求曲线
的方程;
(2)若
、
是曲线
上关于原点对称的两个点,点
是曲线
.上任意-一点(不同于点
、
),当直线
、
的斜率都存在时,记它们的斜率分别为
、
,求证:
的为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b373a7e45d49f5f193f5335bc9602dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b8db072e2b6104671b82f948012fb45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/510cddda-2448-4c58-8e3f-c752f4e7c78e.png?resizew=175)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(2)若
![](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/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.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/67d822262ff00915910e5b87d81ad1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d97dc3b752832906de41447bb58a341.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/6b881044b5c73db6fcce110525741b02.png)
您最近一年使用:0次
解题方法
8 . 在平面直角坐标系xoy中,点A,B的坐标分别是
,直线AM、BM相交于点M,且它们的斜率之积是
.
(1)求 M的轨迹C的方程;
(2)若直线l经过点
,与轨迹C有且仅有一个公共点,求直线l的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42a89dd3c5cc32be2d1adb48309f1132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3389f53711264b0acba3ba6019f8b908.png)
(1)求 M的轨迹C的方程;
(2)若直线l经过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8115c09f801cf0bb02293baef7bf137.png)
您最近一年使用:0次