1 . 已知点
,若过点
的直线
交圆
于
两点,
是圆
上的动点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e8c4afeb6cf6e4eac6c1044ecb12a2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d85223cff466897ee24eeb638219e846.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b085312e6bcc179896073066c879b520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() |
B.![]() ![]() |
C.![]() ![]() |
D.当![]() ![]() ![]() |
您最近一年使用:0次
2023·全国·模拟预测
2 . 已知
是定义域为
的函数,
为奇函数,
为偶函数,当
时,
.若
有5个零点,则实数
的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c4cb9a9b0e8f0cd053c10006abbfd1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4940ae5afa4743c805babbb111cd74df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de8b527865aefa9186462f2ad4a72617.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f4f106a4bb5b00f59a85add9a9633d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/178522b8e568bced46ebad7243d5ac99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
3 . 已知圆M:
,点P为x轴上一个动点,过点P作圆M的两条切线,切点分别为A,B,直线AB与MP交于点C,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa9dd4d452ba05247ea59caf9ad9fa6.png)
A.四边形PAMB周长的最小值为![]() | B.![]() |
C.若![]() ![]() ![]() | D.若![]() ![]() ![]() |
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2021-12-29更新
|
1865次组卷
|
11卷引用:2022届高三普通高等学校招生全国统一考试 数学信息卷(五)
(已下线)2022届高三普通高等学校招生全国统一考试 数学信息卷(五)重庆市第八中学2022届高三下学期调研检测(五)数学试题重庆市万州第二高级中学2023届高三下学期第二次诊断数学试题(已下线)专题18 《圆与方程》中的切线问题(1)-2021-2022学年高二数学同步培优训练系列(苏教版2019选择性必修第一册)山东省滕州市第一中学2021-2022学年高三下学期开学考试数学试题福建省晋江市第一中学2022届高三上学期第三次阶段考数学试题(已下线)数学-2022届高三下学期开学摸底考试卷(山东专用)(已下线)必刷卷04-2022年高考数学考前信息必刷卷(新高考地区专用)(已下线)2.2 直线与圆的位置关系(难点)四川省宜宾市叙州区第二中学校2023-2024学年高二上学期10月月考数学试题(已下线)考点08 相离的位置关系(直线与圆,圆与圆) 2024届高考数学考点总动员
名校
4 . 为解决城市的拥堵问题,某城市准备对现有的一条穿城公路MON进行分流,已知穿城公路MON自西向东到达城市中心点O后转向东北方向(即
).现准备修建一条城市高架道路L,L在MO上设一出入口A,在ON上设一出入口B.假设高架道路L在AB部分为直线段,且要求市中心O与AB的距离为10km.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/21/e6485ac8-6fc3-4af9-a307-ecf8f6b59d3f.png?resizew=250)
(1)求两站点A,B之间距离的最小值;
(2)公路MO段上距离市中心O30km处有一古建筑群C,为保护古建筑群,设立一个以C为圆心,5km为半径的圆形保护区.则如何在古建筑群C和市中心O之间设计出入口A,才能使高架道路L及其延伸段不经过保护区(不包括临界状态)?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ce9433909d7423bcb7a2a8dbc410790.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/21/e6485ac8-6fc3-4af9-a307-ecf8f6b59d3f.png?resizew=250)
(1)求两站点A,B之间距离的最小值;
(2)公路MO段上距离市中心O30km处有一古建筑群C,为保护古建筑群,设立一个以C为圆心,5km为半径的圆形保护区.则如何在古建筑群C和市中心O之间设计出入口A,才能使高架道路L及其延伸段不经过保护区(不包括临界状态)?
您最近一年使用:0次
2020-03-29更新
|
755次组卷
|
3卷引用:【校级联考】江苏省南京金陵中学、海安高级中学、南京外国语学校2019届高三第四次模拟考试数学试题
5 . 已知集合
,
,若
,则实数a的取值范围为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4396bb161137d5583e96fd4fda207c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfe65c8d2bf130c3b4c7c319b872ebaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96f1ba0a1129741502600e47bf058c98.png)
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名校
解题方法
6 . 已知动圆
和定圆
外切,和定直线
相切.
(1)求该动圆圆心
的轨迹
的方程;
(2)过点
的直线
与
交于
两点,在曲线
上存在一点
,使得
为定值,求出点
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bce769d55393c86ae6c312de5158e4b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99c6875d552e9fff3c7d655f3a59b166.png)
(1)求该动圆圆心
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/363598fd39f2269952dc6ddd1201346c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68d40f399c3737563ed161f2b7326a8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
您最近一年使用:0次
7 . 某地拟建造一座大型体育馆,其设计方案侧面的外轮廓如图所示,曲线
是以点
为圆心的圆的一部分,其中
;曲线
是抛物线
的一部分;
,且
恰好等于圆
的半径.假定拟建体育馆的高
(单位:米,下同).
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/18/3db6c469-33cc-437b-93a0-637ea83bb392.png?resizew=156)
(1)若
,
,求
、
的长度;
(2)若要求体育馆侧面的最大宽度
不超过
米,求
的取值范围;
(3)若
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074a95728962a5cf606dce0ccd1b52ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/246518655504f9faaabcda467b8a9f4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4ab7e657f01bdfa235f8c4d6681d13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/186c758f824939fc7de1be6b09506fc5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/18/3db6c469-33cc-437b-93a0-637ea83bb392.png?resizew=156)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/843c9013e16ce26a4be297f1b61419fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b7e0c8d8b6ac10b88aea344bf75a90c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
(2)若要求体育馆侧面的最大宽度
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86608326541db75771f5de9db6187e6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e469fee398e9ef371baf1b91cba2b0eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
您最近一年使用:0次
2020-02-10更新
|
956次组卷
|
3卷引用:2016届上海市徐汇区高三上学期期末学习能力诊断(文)数学试题
名校
8 . 在平面直角坐标系
中,圆
的方程为
,且圆
与
轴交于
两点,设直线
的方程为
.
(1)当直线
与圆
相切时,求直线
的方程;
(2)已知直线
与圆
相交于
两点.(i)
,求直线
的方程;(ii)直线
与直线
相交于点
,直线
,直线
,直线
的斜率分别为
,
,
,是否存在常数
,使得
恒成立?若存在,求出
的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b83d2ed19c67eef71d1a16a3c3fa724c.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/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19e2b6466242aec6c1ff38f83eb66314.png)
(1)当直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)已知直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b73b180c8fa40bf5e4e1ecfb0aae833a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbf434334b09cc0fdd4e86e84e6ceb00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9365bee61c4002828f94cd56c5b34550.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2019-06-15更新
|
1581次组卷
|
3卷引用:【市级联考】江苏省镇江市2019届高三考前模拟(三模)数学试题
9 . 直线
与
轴的交点分别是
直线
与圆
的交点为
给出下面三个结论:①
②
③
.则所有正确结论的序号是_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48ed5adbd356fb0bd4b8d06e31bd041a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9defa23d2a9b88f4dd10e0ea4bef2189.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0310a247af33d7fdd668a74a585290fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dac2b3fb3064c488998bbd68a799eaff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/613c9ed895a96e565ab391f768e88915.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d66bc81ecf797fd81b32809bbb7cc403.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7077b7478f439b06b24353b798b84e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccdc99042080ab815ee50ab5ae588cb3.png)
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2018-04-03更新
|
652次组卷
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4卷引用:2016届山东省师大附中高三最后一模理科数学试卷
10 . 过点
作直线
(
不同时为零)的垂线,垂足为
,点
,则
的取值范围是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18f4ec943ad1319d9df9ead145195817.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04e4dfbb340de3f8441cc9240312814a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dc26c3d0e12c28a398837d5bcfa5654.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/084cf5ffced059f5653ee2a1023518b7.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2018-03-06更新
|
2773次组卷
|
2卷引用:天一大联考2017—2018学年高中毕业班阶段性测试(四)理科数学