1 . 设
,
两点的坐标分别为
,
.直线
,
相交于点
,且它们的斜率之积是
,记点
的轨迹为
.
(1)求
的方程
(2)设直线
与
交于
,
两点,若
的外接圆在
处的切线与
交于另一点
,求
的面积.
![](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/6fd0825e68122a65426840fbf07cf296.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00ed24bfcc37b79fe9ca61ed8fdf26ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d78fd95f89dec2d373fa57f02acd739f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c105d6ba18fbb0581fb982175e2eac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad3cd61d00f89e68ccca2cac5c937783.png)
您最近一年使用:0次
2 . 已知动圆
与圆
外切,同时与圆
内切;则动圆圆心
的轨迹方程为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c88750ae8bdb3eea4be08ba8930bf52a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2872653277ec3bd11c4e2175690ce9bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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名校
3 . 设
分别是直线
和
上的两个动点,并且
,动点
满足
.动点
的轨迹方程为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6617bfdc4ae73c1cc0a4767d5c881f38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4de5dbdaa3560b2c85ef4c568d80c7f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94745b50f9315e478ab5cc64cf9988ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98094053649f93909ac555de3694ad52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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名校
解题方法
4 . 在平面直角坐标系
内,动点
与定点
的距离和它到定直线
的距离的比是
.
(1)求动点
的轨迹方程.
(2)若
为动点
的轨迹上一点,且
,求三角形
的面积.
![](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/16fd15503ee692f8286b0312f7c6f0cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/224d30ca84f1aeeeda7a718e751a4925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55d78a58077822fb74b7b482e43d2ba1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/002ed1ebb2cb936e10ab478789f91c7c.png)
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2023-11-11更新
|
1249次组卷
|
4卷引用:天津市汇文中学2023-2024学年高二上学期期中数学试题
天津市汇文中学2023-2024学年高二上学期期中数学试题贵州省遵义市桐梓县荣兴高级中学2023-2024学年高二上学期第三次月考数学试题广东省鹤山市第一中学2023-2024学年高二上学期第二阶段考试数学试题(已下线)专题20 椭圆的标准方程5种常见考法归类 - 【考点通关】2023-2024学年高二数学高频考点与解题策略(人教B版2019选择性必修第一册)
名校
5 . 设圆
与
:
外切并与
:
内切,则
的圆心轨迹为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e383fcc122f267043fbafe0972bfb900.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4f6f74444b2b7947fc6e35c8d62322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6afc954e87bd737ec051d5c94837c8a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.圆 | B.椭圆 | C.双曲线 | D.抛物线 |
您最近一年使用:0次
6 . 如图,已知定点
,点P是圆C:
上任意一点,线段PD的垂直平分线与半径CP相交于点M.
![](https://img.xkw.com/dksih/QBM/2022/4/27/2967324612526080/2968150567337984/STEM/9985e9db1e704db1bdda3d76daf62794.png?resizew=163)
(1)当点P在圆上运动时,求点M的轨迹方程;
(2)过定点
且斜率为k的直线l与M的轨迹交于A、B两点,若
,求点O到的直线l的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f49402c4ddc06c4a5f9c83ee6a20f2da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3bf1f7538aa15626bab82fe5cc65e0c.png)
![](https://img.xkw.com/dksih/QBM/2022/4/27/2967324612526080/2968150567337984/STEM/9985e9db1e704db1bdda3d76daf62794.png?resizew=163)
(1)当点P在圆上运动时,求点M的轨迹方程;
(2)过定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c83a0d65b095449acf3519d7855cb42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bb8d93527283bdc2b994728f6f49a0a.png)
您最近一年使用:0次
解题方法
7 . 两圆
,
.动圆
在圆
内部且与圆
相内切,与圆
相外切,求动圆圆心
到原点
的距离的最大值________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/181d815ea6b3e47a851323260842505e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/722defb8c7dbbc7c8637d2290a2b5561.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/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
您最近一年使用:0次
8 . 已知B(
,0)是圆A:
内一点,点C是圆A上任意一点,线段BC的垂直平分线与AC相交于点D.则动点D的轨迹方程为_________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47153fdd73c0661fa460130082e30929.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a319f4db607f87ff964eb67d0cbebe1a.png)
您最近一年使用:0次
2022-03-31更新
|
1382次组卷
|
6卷引用:天津市部分区2021-2022学年高二上学期期末数学试题
天津市部分区2021-2022学年高二上学期期末数学试题(已下线)第13讲 椭圆(1)(已下线)第13讲 椭圆(2)(已下线)第05讲 椭圆 (高频考点,精讲)-1河南省焦作市第十一中学2023-2024学年高二上学期11月月考数学(已下线)专题01圆锥曲线中的求方程问题(三大题型)
名校
解题方法
9 . 已知圆
:
,圆
:
,动圆C与圆
和圆
均内切.
(1)求动圆圆心C的轨迹E的方程
(2)点
(
)为轨迹E上的点,过点P作两条直线与轨迹E交于AB两点,直线PA,PB的斜率互为相反数,则直线AB的斜率是否为定值?若是,求出定值:若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/381fb9decbab03b6b9d41975e320a065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e383fcc122f267043fbafe0972bfb900.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(1)求动圆圆心C的轨迹E的方程
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0632becd411a505efaf6ce37b6aada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fff6e7e2b9f2b68b1647f6350b98dc8.png)
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2022-03-13更新
|
696次组卷
|
3卷引用:天津市河北区2021-2022学年高三上学期期末数学试题
天津市河北区2021-2022学年高三上学期期末数学试题河南省郑州市第四高级中学2021-2022学年高二下学期第二次调研考试数学(文)试题(已下线)专题29 圆锥曲线的轨迹问题5种常见考法归类 - 【考点通关】2023-2024学年高二数学高频考点与解题策略(人教A版2019选择性必修第一册)
10 . 在平面直角坐标系
中,已知点
,
,直线
与直线
的斜率之积为
,记动点
的轨迹为曲线
.
(1)求曲线
的方程;
(2)若点
为曲线
上的任意一点(不含短轴端点),点
,直线
与直线
交于点
,直线
与
轴交于点
,记直线
的斜率为
,直线
的斜率为
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd99c5000629d7f49499d666e68f40d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852b303689c31189cd47bb4a3220f9fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/602baac86c2b1668ecdfadc8a5948885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5fcce10d4243fb2a8351db179c2c48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a424b50eaeafa6f302ffd95476cb86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d454c82d9e52747563d47b68099249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27e66b12019cdf68327d34c90dff7c04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00b3ebbb4668794a2ed95c621f63f318.png)
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2022-01-20更新
|
910次组卷
|
2卷引用:天津市新华中学2022届高三下学期3月统练5数学试题