1 . 已知圆
和圆
,过动点
分别作圆
,圆
的切线
,
(A,
为切点),且
,则
的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/560adea7b0d4fbe4131fc41f3fcbd871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2390c3620d076f200ec790b8d0c09a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb5c4882a2713d22cc8bb19cc51548b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ce5dcaffd91bc44cda4a2e44000ae73.png)
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2 . 已知动点
在抛物线
上,过点
引圆
的切线,切点分别为A、B,则
的最小值为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b84df2d39fa36c3f4ee72a0817fd2b25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaff41080fdea43eea7efedf9ebc1498.png)
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3 . 过点
作圆O:
的两条切线,则两条切线夹角的正弦值为______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f13bf66fc845b115de4ec45b4be0e23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
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名校
4 . 已知P为直线
上一动点,过点P作圆
的切线,切点分别为A,B,则当四边形PAOB面积最小时,直线AB的方程为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bc8e0a4e596e6b0a2f81e1f03fa0430.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79382ba44ba669b5d43fdd5427adf16c.png)
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5 . 过抛物线
的焦点
作圆
的两条切线,切点分别为
,
,若
为等边三角形,则
的值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3764ba3aa0a241787f4661026bb14053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb8f39c669699aef9d2a48277f90adda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91a9bf6bda9363dbef5f6ff4bf6a5edf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
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2024-01-25更新
|
111次组卷
|
2卷引用:四川省凉山州2023-2024学年高二上学期期末检测数学试卷
名校
6 . 已知直线
是圆
的对称轴,过点
作圆
的一条切线,切点为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c84a09595eabd6ae21a2e8faa7465c.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edaea60e93342e9c54914d894858fd7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12e6a95d85a6bfc628a8e63dd71ffcd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d02aa702406987fbeb90f0ab7ea1f8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c84a09595eabd6ae21a2e8faa7465c.png)
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2023-12-19更新
|
531次组卷
|
4卷引用:辽宁省辽阳市2024届高三上学期期末数学试题
辽宁省辽阳市2024届高三上学期期末数学试题贵州省2023-2024学年高二上学期12月月考数学试题(已下线)专题02 直线与圆的综合应用问题(九大考点)-【寒假自学课】2024年高二数学寒假提升学与练(人教A版2019)江西省景德镇市景德镇一中2024届高三上学期1月考试数学试题
名校
7 . 抛物线
上有一动点
,过
作曲线
的切线,其中一个切点为
,则
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0261104a7c308433a0c0508ff20ea29a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48b9a9a9962efa3f70582ace8588b5c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d063ec7f9dbeba72fabf4437f9400e07.png)
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2023-11-23更新
|
246次组卷
|
3卷引用:江西省吉安市2023-2024学年高二上学期期末教学质量检测数学试题
名校
8 . 已知动点
在椭圆
上,过点P作圆
的切线,切点为M,则
的最小值是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e78f1a9cc4dedc05c175ab99b288b9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7da196171d6e7da45d6636e91bd59d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d341082cc54b1cb7a790af9ec4a365d.png)
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2023-11-15更新
|
737次组卷
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3卷引用:黑龙江省哈尔滨师范大学附属中学2023-2024学年高二上学期期末考试数学试题
名校
9 . 已知点
在圆
上,点
、
,则点
到直线
的距离的最大值为____________ ;当
最大时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/255b03f01d1039f11f5a3ba36bce5789.png)
____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec23fae7cb8d42f46575efaf589df91b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e95e84f5c91c910aaafc5e74dbfbdf59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29610a3415c1e795d35979a5a9ff69f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09bebb16c0ffc99a945619ae0986cadd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/255b03f01d1039f11f5a3ba36bce5789.png)
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2023-11-02更新
|
255次组卷
|
3卷引用:云南省保山市、文山州2023-2024学年高二上学期1月期末质量监测数学试题
10 . 过
作圆
与圆
的切线,切点分别为
,
,若
,则
的最小值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8701e0cce437edc830438b4fe6277d89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/187796700eb5500018a4e0f0a2ca4325.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d6f517c4f44c877afa7f583a3827b36.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/39ee433f07e8fba1e037ced700b33c5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29ebc856291255f2d4a6c20b982a2442.png)
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2023-09-09更新
|
1102次组卷
|
10卷引用:河南省三门峡市2022-2023学年高二上学期期末数学试题
河南省三门峡市2022-2023学年高二上学期期末数学试题(已下线)模块二 专题4 巧用几何意义解决直线与圆中的最值问题 期末终极研习室高二人教A版(已下线)期末精确押题之填空题(40题)-2023-2024学年高二数学上学期《考点·题型·难点》期末高效复习(人教A版2019)(已下线)2.2 直线与圆的位置关系(10大题型)-【题型分类归纳】2023-2024学年高二数学同步讲与练(苏教版2019选择性必修第一册)(已下线)第2章 圆与方程章末题型归纳总结(2)(已下线)高二上学期第一次月考填空题压轴题50题专练-2023-2024学年高二数学举一反三系列(人教A版2019选择性必修第一册)(已下线)专题突破卷22 求圆的最值与范围(已下线)单元提升卷10 平面解析几何(已下线)模块三 专题2 直线与圆的最值问题(高一人教A)(已下线)2.5.1 直线与圆的位置关系 精讲(10大题型)-【题型分类归纳】2023-2024学年高二数学同步讲与练(人教A版2019选择性必修第一册)