名校
解题方法
1 . 如图,已知圆
,点
为直线
上一动点,过点
引圆
的两条切线,切点分别为
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/17/1b303747-fd06-4341-a2de-082c76515e8a.png?resizew=280)
(1)求直线
的方程,并判断直线
是否过定点
若是,求出定点的坐标,若不是,请说明理由;
(2)求线段
中点的轨迹方程;
(3)若两条切线
,
与
轴分别交于
,
两点,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/608dc153e32a3368d4fd02aac6739ede.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/350d8add927871a7d66eef1e42624fb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3aab32903fc13d099bf398366be37fb.png)
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/17/1b303747-fd06-4341-a2de-082c76515e8a.png?resizew=280)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82bbee662e242611afdbdae4b8a36a7c.png)
(2)求线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(3)若两条切线
![](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/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a670d12554358604dc27abf2eaf1732.png)
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9卷引用:辽宁省大连市滨城高中联盟2023-2024学年高二上学期期中考试数学试题
辽宁省大连市滨城高中联盟2023-2024学年高二上学期期中考试数学试题湖南省益阳市2022-2023学年高二上学期10月联考数学试题浙江省宁波市北仑中学2022-2023学年高二上学期期中数学试题(2-10班+外高班使用)广东省珠海市斗门区第一中学2022-2023学年高二上学期期中数学试题(已下线)期中押题预测卷(考试范围:选择性必修第一册)(拔高卷)-【单元测试】2022-2023学年高二数学分层训练AB卷(人教B版2019)福建省漳州市漳浦立人学校2022-2023学年高二上学期期中考试数学试题(已下线)专题05 直线与圆综合大题18种题型归类-【巅峰课堂】2023-2024学年高二数学上学期期中期末复习讲练测(人教A版2019选择性必修第一册)(已下线)专题02 期中真题精选(压轴93题10类考点专练)(2)(已下线)圆 与方程
名校
2 . 已知曲线
在点
处的切线
与圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d8fa9b6a6550d03e7aa6d7950bb96e1.png)
也相切,当半径
最大时圆的方程是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f2eff609c6043c2a89a6dd163fe2244.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50eafb7845a46236b3f3ad4ac574a888.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d8fa9b6a6550d03e7aa6d7950bb96e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/445489a1d1c2f9a53608c7121d42f02b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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4卷引用:辽宁省沈阳市第二中学2024届高三下学期开学考试数学试题
辽宁省沈阳市第二中学2024届高三下学期开学考试数学试题东北师范大学附属中学2021届高三年级第五次模拟考试理科数学试题(已下线)考点39 直线与圆、圆与圆的位置关系-备战2022年高考数学(理)一轮复习考点帮(已下线)专题10 切线问题【讲】
名校
3 . 如图,已知定圆
,定直线
过
的一条动直线
与直线
相交于
,与圆
相交于
两点,
是
中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/22/3c884cb1-5f9f-403e-ae1e-c7f773ae969b.png?resizew=187)
(1)当
与
垂直时,求证:
过圆心
;
(2)当![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c84a09595eabd6ae21a2e8faa7465c.png)
时,求直线
的方程;
(3)设![](https://staticzujuan.xkw.com/quesimg/Upload/formula/825116eb345f5505ebc8c1cdb8a1f131.png)
,试问
是否为定值,若为定值,请求出
的值;若不为定值,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e85fc19d652ea7c8cd9236a17fc9c306.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d2ecbf4eeb997be8293cadc7f71216.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc304df70be14cccc9abea2c91e2fdb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dd8cb171425253834dfd7fa1a9da9ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/22/3c884cb1-5f9f-403e-ae1e-c7f773ae969b.png?resizew=187)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c84a09595eabd6ae21a2e8faa7465c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/825116eb345f5505ebc8c1cdb8a1f131.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecdc7bdc6448ef9a13c59fdce1b9bb57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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2020-01-06更新
|
765次组卷
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5卷引用:2014-2015学年辽宁省朝阳区三校高二下学期第一次段测理科数学试卷
4 . 已知点
在曲线
上,则
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba7204f43679af6935e494c59d40c6ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75db6f4115857bc0041da949ba5f95a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/367e79286a07d4b4349255b3d053e2c1.png)
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1473次组卷
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2卷引用:辽宁省沈阳市法库县高级中学2020-2021学年高二上学期10月月考数学试题
名校
解题方法
5 . 已知平面直角坐标内定点
,
,
,
和动点
,
,若
,
,其中O为坐标原点,则
的最小值是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65c09b7a163e7bf1ee295d7297286afa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a54417a9e9b5242841bebe000870cb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10f425201dc93f18835d42a2e47de589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3632df748c002736b8fd007d43fedc13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9fcbc60ae6257d13f1678aef9e46f36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f8b3e05c886a3d71eb09c7639001414.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e96fc4fb850f0a3fea90bd54d33b0b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb785e08831d3377c081fe5e97492c4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c41f27303ef21d296e6e1d0a46177323.png)
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2018-07-07更新
|
1877次组卷
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5卷引用:辽宁省大连市一〇三中学2020-2021学年高二10月月考数学试题
6 . 如图,正方体
的棱长为1,
分别为线段
上两个动点且
,则下列结论中正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/7/990bc70e-a66a-4b77-900e-f000bd5caf79.png?resizew=167)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/450176ba93397527fc3520c55dd1476a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db37b5ce697dab3189a15881d00fcd0e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/7/990bc70e-a66a-4b77-900e-f000bd5caf79.png?resizew=167)
A.存在某个位置![]() ![]() |
B.存在某个位置![]() ![]() ![]() |
C.三棱锥![]() |
D.![]() ![]() |
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2018-02-17更新
|
1020次组卷
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2卷引用:辽宁省大连市庄河市高级中学2022-2023学年高二上学期12月月考数学试题
名校
7 . 已知圆
:
,
是
轴上的动点,
分别切圆
于
两点.
(1)若
,求
及直线
的方程;
(2)求证:直线
恒过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51ecf7a6913d90c2df051d608011cc57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92ca520748c8b8d3878fb112a89ada7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f500666f8b442310f6136495476b32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaa1dda145970b83587dbcb8e46987ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2dca049735b45fb9b2533c68605eddc.png)
(2)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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