名校
1 . 已知O为坐标原点,点P在标准单位圆上,过点P作圆C:
的切线,切点为Q,则
的最小值为_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/340e9eac0866ece3535f098929d2be4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d44e8bc37ed03f44470762748a8f942a.png)
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2023-12-22更新
|
762次组卷
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4卷引用:北京市第五十七中学2023届高三上学期12月月考数学试题
北京市第五十七中学2023届高三上学期12月月考数学试题湖南省长沙市雅礼中学2024届高三上学期月考数学试题(四)(已下线)专题17 圆锥曲线常考压轴小题全归类(16大题型)(练习)(已下线)重难点7-1 圆的最值与范围问题(8题型+满分技巧+限时检测)
2 . 点
是直线
上的动点,过点
作圆
的切线,分别相切于
、
两点,则
的最小值为____________ ;四边形
面积的最小值为____________ ;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aed96fd65471bd059ad486380a3fdc48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f5d967ad135991b6075ee45df55643.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/d063ec7f9dbeba72fabf4437f9400e07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/771a7a9e485517a3c1a529608104f32f.png)
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3 . 过点
作圆
的两条切线,切点分别为M,N,则直线
的方程为_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bcc512ec11bf8f6e0f42977dec712c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a60dac104613d9caefacddc3963d266.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
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2023-03-30更新
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749次组卷
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2卷引用:广东省深圳市光明区2022-2023学年高二上学期期末数学试题
名校
4 . 已知
为坐标原点,圆
:
,圆
上到直线
的距离等于1的点最多有______ 个,过直线
上任一点
作圆
的切线,切点为A,
,则四边形
面积的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/409e1c4ec5676366a00032317a7c3c78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06eecac8dd7105ca172efe2e88336626.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9c75d0f8a8d94c8589a5a1ca18709cd.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec51d1ad99e9e93296c43ed1b2b8ed5e.png)
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5 . 在平面直角坐标系
中,过
轴上的点
分别向圆
和圆
引切线,记切线长分别为
、
.则
的最小值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a7a8914998801434596a2b0192288cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/621c64ae1835893612357f1ff455194e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5edf900c810371fb21297c15f86d8743.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b31ac1def558351e2e3ed1235c570530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2a4b32d388558eb9a9e4f0f2dd57c09.png)
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名校
6 . 已知O为坐标原点,抛物线
与抛物线
在第一象限内的交点为
,若点P在圆
上,且直线OP与圆C相切,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a59203badfd97c27a187b71dfcc3139.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9943617f89cb9a02d0fb233aa3f90b68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a788754dde2c31d5eb02fae200aa100f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf0d139c9810361b4971904a943856b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf00a9e97b4e278a2fa10257d2b73fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a59203badfd97c27a187b71dfcc3139.png)
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名校
解题方法
7 . 过点
作圆
的两条切线,切点分别为M,N,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e3d627f5fbd04271389d503942d233.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d00d5d8cc31aaca7fc2eafb99eac7629.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79382ba44ba669b5d43fdd5427adf16c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e3d627f5fbd04271389d503942d233.png)
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2022-12-03更新
|
606次组卷
|
4卷引用:湖北省武汉市部分重点中学2022-2023学年高二上学期期中联考数学试题
名校
8 . 已知圆C上的任意一点到两个定点
,
的距离之比为
,则圆C的方程是___________ ;在直线
上存在点P满足:过P作圆C的切线,切点分别为M,N,且四边形PMCN的面积为
,则实数m的取值范围是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/448c0a5ee776d19ce8e42ac9a5fd27c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2c77a42750684cb6157c2c7fb9422a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/692265c4b64c721bd3e567b8af832b7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41322821ce31416fdac8dd6e0aa41c71.png)
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2022-11-26更新
|
180次组卷
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5卷引用:河南省部分名校2022-2023学年高二上学期11月联考数学试题(A卷)
9 . 若点P在直线
上移动,过P作圆
的切线,切点分别为A,B,则
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24fa9a65310284f284b6b067a2df301c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
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10 . 在圆幂定理中有一个切割线定理:如图1所示,QR为圆O的切线,R为切点,QCD为割线,则
,如图2所示,在平面直角坐标系xOy中,已知点
,点P是圆
上的任意一点,过点
作直线BT垂直AP于点T,则
的最小值是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3466cd6a5bb8eed21baba9d6dc0da81f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/311497849126f1aaf1da0ec75602eabf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79382ba44ba669b5d43fdd5427adf16c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1b47e7bf02b3ca16f7d96b9369e51a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49f7d4ad11577ced2a442909cba1510c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/20/b9e855d0-62d6-4f42-8e76-9d91341cc9a4.png?resizew=385)
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