解题方法
1 . 已知圆C,圆
,圆
这三圆有一条公共弦.
(1)当圆C的面积最小时,求圆C的标准方程;
(2)在(1)的条件下,直线l满足:
(ⅰ)与直线
平行;
(ⅱ)与圆C相切.
若直线l与圆
分别交于A,B两点,与圆
分别交于D,E两点,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d6ac185918af575c60aa91b070ee612.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88002107328c7669fe3cb5fdeb14efd8.png)
(1)当圆C的面积最小时,求圆C的标准方程;
(2)在(1)的条件下,直线l满足:
(ⅰ)与直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89646b149f703d83ea142d297bfffb46.png)
(ⅱ)与圆C相切.
若直线l与圆
![](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/991444dcdadfebbef3208c68467c13e2.png)
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解题方法
2 . 如图,点
,
,
,
是以
为直径的半圆,
是以
为直径的半圆,
是以
为直径的半圆,三段弧构成的曲线记为
,给出下列四个结论:
①曲线
围成的图形面积为
;
②
所在圆与
所在圆的公共弦的弦长为
;
③过点
的直线
与
所在圆相交所得弦长为2,则直线
的方程为
,或
;
④直线
与
所在圆相交于
,
两点,则
,
.
其中所有正确结论的序号是_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/448c0a5ee776d19ce8e42ac9a5fd27c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29610a3415c1e795d35979a5a9ff69f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49dd31773f55719ebd91ed3389d0de68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed41d321f4c0717ac5b443aad942d9a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/667349d99185bb045030b733352ff7fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
①曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a0209c599c13d645a2bd672ebe4fa06.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed41d321f4c0717ac5b443aad942d9a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/667349d99185bb045030b733352ff7fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
③过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c7f6a03826a5ad351c1f7ca553a6945.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c854f1724e33a2706282c945ef320a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
④直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e8a3365e99f926b1dafa901ab232152.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed41d321f4c0717ac5b443aad942d9a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8198c3b302b3820e86763428eb1e91cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3463ced6030af957f13f9ba05b977c1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e27ec4efc046f109816f223df09fd77f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cc33cc8cca3772341f48ddcceb016b8.png)
其中所有正确结论的序号是
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/5/b5b2c74c-e3c3-4c3c-b48f-5734ae3b3dd6.png?resizew=193)
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22-23高三上·江西南昌·阶段练习
解题方法
3 . 已知圆
.
(1)若圆C被直线
截得的弦长为8,求圆C的直径;
(2)已知圆C过定点P,且直线
与圆C交于A,B两点,若
,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2165b5ad20619d838f204f200801e22b.png)
(1)若圆C被直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/874188b1ad1af65fe2951e3a0c1c0e84.png)
(2)已知圆C过定点P,且直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9378192d39a3089b92ea7cc8a44c667a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66a3af6175f323f7e1bfee6609cb8513.png)
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7卷引用:河南省豫南名校2022-2023学年高二上学期期中联考数学试题
4 . 已知圆
:
,点
是圆
上一点,点P为直线
上的动点,过点
作圆
的切线,切点为M、N.
(1)求过点
的圆
的切线方程;
(2)以P为圆心的圆交圆
于M、N两点,问直线MN是否恒过一定点?若过定点求出定点坐标.
(3)求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/701f3b0e2bedfe5195443459072d798e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/225c29739603479b4b13a64bf93679d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c33bddb7f235b131a5391ea650dae89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/701f3b0e2bedfe5195443459072d798e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1989fe3e19c8487a0f0e0b42f54c45dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc5c19ac440746be97d8b46af5d288a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/701f3b0e2bedfe5195443459072d798e.png)
(1)求过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c33bddb7f235b131a5391ea650dae89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/701f3b0e2bedfe5195443459072d798e.png)
(2)以P为圆心的圆交圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/701f3b0e2bedfe5195443459072d798e.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc8e9adbace750044447ccd4ddd7ed3d.png)
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名校
解题方法
5 . 在平面直角坐标系中,
,
,
,
,设点
的轨迹为
,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d284169b51a836bb3dcf56ba0227bd6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/530310ea362861513ad5a9d0b4261558.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c92b3b6b806de22277e758e4a57a85c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7194dca22e8a56ac0c9d67bfd7eff4e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.轨迹![]() ![]() |
B.![]() ![]() |
C.![]() ![]() |
D.若直线![]() ![]() ![]() ![]() ![]() |
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5卷引用:湖南省益阳市2022-2023学年高二上学期10月联考数学试题
名校
解题方法
6 . 已知圆M:
,直线l:
,直线l与圆M交于A,C两点,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a85e8f5c77fb05ccb0e9403667c1ba7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/757f055a6bb9317021f66beb82ecfcd5.png)
A.直线l恒过定点![]() |
B.![]() |
C.![]() ![]() |
D.当![]() ![]() |
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10卷引用:福建省南平市建阳第二中学2022-2023学年高二上学期第一次月考数学试题
福建省南平市建阳第二中学2022-2023学年高二上学期第一次月考数学试题江西省临川第一中学2022-2023学年高二上学期期中质量监测数学试题广东仲元中学2022-2023学年高二上学期期中数学试题(已下线)突破2.5 直线与圆、圆与圆的位置关系(重难点突破)-【新教材优创】突破满分数学之2022-2023学年高二数学重难点突破+课时训练湖北省武汉市2022届高三下学期五月模拟(二)数学试题(已下线)专题25 圆中的范围与最值问题-2(已下线)考向33 一类与圆有关的最值与范围问题(七大经典题型)江苏省南通市海安市立发中学2022-2023学年高三上学期九月检测数学试题福建省厦门双十中学2023届高三高考适应性考试数学试题(已下线)第四节 直线与圆、圆与圆的位置关系 核心考点集训
7 . 在①直线
与
、
均相切,②直线
截
、
、
所得的弦长均相等,这两个条件中任选一个,补充在下面问题中,并求解该问题.
问题:
年是中国传统的农历“鼠年”,现用
个圆构成“卡通鼠”的头像.如图,
是
的圆心,且
过原点;点
、
在
轴上,
、
的半径均为
,
、
均与
外切.直线
过原点.若___________,求直线
截
所得的弦长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6f6558fef858bf27e9811c2d9426fe7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/669e8dfb2b45e6f74d86408343a18fe2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c20d0b44025a639ce3a92d639dae587.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6f6558fef858bf27e9811c2d9426fe7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/669e8dfb2b45e6f74d86408343a18fe2.png)
问题:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/701554763bdbbf2689a8dae07608da38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a23e87d16c32b5aa4357f481b5808a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c20d0b44025a639ce3a92d639dae587.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c20d0b44025a639ce3a92d639dae587.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6f6558fef858bf27e9811c2d9426fe7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/669e8dfb2b45e6f74d86408343a18fe2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6f6558fef858bf27e9811c2d9426fe7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/669e8dfb2b45e6f74d86408343a18fe2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c20d0b44025a639ce3a92d639dae587.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c20d0b44025a639ce3a92d639dae587.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/3/789556d6-b1cc-4c0b-843d-3fc35320bb36.png?resizew=218)
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6卷引用:沪教版(2020) 选修第一册 新课改一课一练 第2章 2.1.3圆的一般方程
沪教版(2020) 选修第一册 新课改一课一练 第2章 2.1.3圆的一般方程(已下线)第2章 圆与方程综合测试-【暑假自学课】2022年新高二数学暑假精品课(苏教版2019选择性必修第一册)(已下线)第2章 圆与方程(A卷·知识通关练)(1)(已下线)专题2.16 圆与圆的位置关系-重难点题型检测-2022-2023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)2.5.2 圆与圆的位置关系练习(已下线)专题8-1 直线与圆归类(讲+练)-2
8 . 我们知道:当
是圆O:
上一点,则圆O的过点
的切线方程为
;当
是圆O:
外一点,过
作圆O的两条切线,切点分别为
,则方程
表示直线AB的方程,即切点弦所在直线方程.请利用上述结论解决以下问题:已知圆C的圆心在x轴非负半轴上,半径为3,且与直线
相切,点
在直线
上,过点
作圆C的两条切线,切点分别为
.
(1)求圆C的方程;
(2)当
时,求线段AB的长;
(3)当点
在直线
上运动时,求线段AB长度的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf0d139c9810361b4971904a943856b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3503d330608e7138d1b529aba4512fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d340bd3f078b9261238d4fe59f1473c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf0d139c9810361b4971904a943856b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3503d330608e7138d1b529aba4512fa.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/d340bd3f078b9261238d4fe59f1473c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be0c30f0fa70877bc4c120070d9f6ba7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/642babc2f4fe7d6358c7b5d52fb32c1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
(1)求圆C的方程;
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/614bbb60ee52983905473ae49c690957.png)
(3)当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/642babc2f4fe7d6358c7b5d52fb32c1b.png)
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解题方法
9 . 已知直线
,圆C的方程为
,则下列选项正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/536df29671676f943ede34fc11c4e468.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04b857e290b531463eca3226e435ec96.png)
A.直线l与圆一定相交 |
B.当k=0时,直线l与圆C交于两点M,N,点E是圆C上的动点,则![]() ![]() |
C.当l与圆有两个交点M,N时,|MN|的最小值为2![]() |
D.若圆C与坐标轴分别交于A,B,C,D四个点,则四边形ABCD的面积为48 |
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2022-03-09更新
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3卷引用:湖南省岳阳市岳阳县第一中学2021-2022学年高二下学期第一次阶段考试数学试题