名校
解题方法
1 . 已知以点
为圆心的圆经过原点
,且与
轴交于点
,与
轴交于点
.
(1)求证:
的面积为定值.
(2)设直线
与圆
交于点
,
,若
,求圆
的方程.
(3)在(2)的条件下,设
,
分别是直线
和圆
上的动点,求
的最小值及此时点
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f4b7f273d813a17f6a3a0a5592cd2af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/056e249d0c33ef92b956f84937fa9324.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab760f42892e987055c09495bd014554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(3)在(2)的条件下,设
![](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/d4958a3ab5b7a862f715b14822710b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01881ba4fd330f2d1c95374c89b50ae9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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2024·全国·模拟预测
解题方法
2 . 已知
,
,
,若过点A的直线l、直线BC及x轴正半轴y轴正半轴围成的四边形有外接圆,则该圆的一个标准方程为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/448c0a5ee776d19ce8e42ac9a5fd27c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/316ba5cbb31299d683ac6c7dd795db85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dc03fafb03395ed84030f03c5d93aa3.png)
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名校
解题方法
3 . 已知点
,
,以线段
为直径的圆的标准方程为_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ba4e42b66076aa90f5b895b3ce59033.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7daab97b3dbeb08081c3c36e8fc5cbba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
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解题方法
4 . 已知点
是圆 C
上的任意一点,则
的最大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23de6753f49f1ad682fddc5f31534bbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0649196c51a7656b0e2677c2940057d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a00a967a47547ed32e36e8d395dfa425.png)
A.25 | B.24 | C.23 | D.22 |
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5 . 圆
的圆心到直线
与直线
的距离相等,则实数
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e9ca23fdfec09b54ee1c5275212d3ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c50866229ec5a3640fb250f9bd2192b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
A.![]() | B.1或![]() | C.![]() | D.3 |
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解题方法
6 . 由动点
向圆
引两条切线
,切点分别为
,若四边形
为正方形,则动点
的轨迹方程为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d78849358b593fb45a590b01ebe382db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790ef3382b1c731f2885eecfd92c2a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce55d12917b2c9372e6786238df3b7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近半年使用:0次
解题方法
7 . 如图1所示,为曲杆道闸车库出入口对出人车辆作“放行”或“阻拦”管制的工具.它由转动杆
与横杆
组成,
为横杆的两个端点.在道闸抬起的过程中,横杆
始终保持水平.如图2所示,以点
为原点,水平方向为
轴正方向建立平面直角坐标系.若点
距水平地面的高度为1米,转动杆
的长度为1.6米,横杆
的长度为2米,
绕点
在与水平面垂直的平面内转动,与水平方向所成的角
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49cbbf0efc7ec76c6596103068350ba7.png)
A.则点![]() ![]() ![]() |
B.则点![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() ![]() ![]() |
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名校
8 . 将斜边长为
的等腰直角三角板放在平面直角坐标系中,且使其中一个顶点与原点重合,一条边落在
轴的正半轴上,则该三角板外接圆的一个标准方程可以为_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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2024-04-17更新
|
142次组卷
|
3卷引用:宁夏固原市第一中学2024届高三下学期模拟考试文科数学试题(一)
解题方法
9 . 已知圆
关于直线l对称的圆为圆
,则直线l的方程为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bf7d969ee6f3131219a0ae5d40e971e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd8407963d4114a4433b7a642f852197.png)
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名校
10 . 已知
(
,
),定义方程
表示的是平面直角坐标系中的“方圆系”曲线,记
表示“方圆系”曲线
所围成的面积,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d1eabb2069a21779950099f1f8b98e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e167b43045b3297248e334c41c621b8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b00438433719b82971f9fe309e04b5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/211d9f06beb790d5b943e59c692df970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/211d9f06beb790d5b943e59c692df970.png)
A.“方圆系”曲线![]() |
B.![]() |
C.![]() |
D.“方圆系”曲线![]() ![]() |
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