2023高三·全国·专题练习
解题方法
1 . 用多种方法推导圆的标准方程:
,圆心为
,半径为r.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b353454a5807af1cf768f43245197c8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
您最近一年使用:0次
解题方法
2 . 街头有一片绿地,绿地如图所示(单位:
),其中
为圆弧,求此绿地面积(精确到
).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15e00f40396e914d1d9955bd7785f1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e71f8c680db71a63225b2fa75d73c3f0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/5/b49434de-ef02-42d3-a32a-39bc7c067199.png?resizew=143)
您最近一年使用:0次
解题方法
3 . 如图是一座类似于上海卢浦大桥的圆拱桥示意图,该圆弧拱跨度
为
,圆拱的最高点
离水面
的高度为
,桥面
离水面
的高度为
.
(1)建立适当的平面直角坐标系,求圆拱所在圆的方程;
(2)求桥面在圆拱内部分
的长度.(结果精确到
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce3fedeef066be493469797b2ccae39f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f631cfdf4666db95beb923072ced8d95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c56c87fd6bf8a44244ba51a9d244e22.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/26/ce9fdc6b-bfb0-4f6e-bd55-9f261bc54f21.jpg?resizew=223)
(1)建立适当的平面直角坐标系,求圆拱所在圆的方程;
(2)求桥面在圆拱内部分
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfaa19eeaf415ed419e77fe92794f443.png)
您最近一年使用:0次
2023-06-20更新
|
955次组卷
|
7卷引用:上海市静安区2022-2023学年高二下学期期末数学试题
上海市静安区2022-2023学年高二下学期期末数学试题第二章 直线和圆的方程 (练基础)(已下线)第08讲 2.4.2圆的一般方程(10 类热点题型讲练)-【帮课堂】2023-2024学年高二数学同步学与练(人教A版2019选择性必修第一册)(已下线)专题2.9 直线与圆的方程大题专项训练(30道)-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)2.1 圆的方程(八大题型)-【帮课堂】2023-2024学年高二数学同步学与练(苏教版2019选择性必修第一册)(已下线)专题17 直线与圆的位置关系9种常见考法归类- 【考点通关】2023-2024学年高二数学高频考点与解题策略(人教B版2019选择性必修第一册)(已下线)通关练11 圆的方程大题10考点精练(47题)- 【考点通关】2023-2024学年高二数学高频考点与解题策略(人教A版2019选择性必修第一册)
2023高三·全国·专题练习
解题方法
4 . 如图,足球门框的长
为
,设足球为一点
,足球与
,
连线所成的角为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/5/7047088d-a8b3-4bd5-9cc7-dd86cf558713.png?resizew=195)
(1)若队员射门训练时,射门角度
,求足球所在弧线的方程;
(2)已知点
到直线
的距离为
,到直线
的垂直平分线的距离为
,若教练员要求队员,当足球运至距离点
为
处的一点时射门,问射门角度
最大可为多少?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23ca8554d115ba7b0b7d06d98148f14c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/8b40aa8d2482d698ebef69cf225f99f8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/5/7047088d-a8b3-4bd5-9cc7-dd86cf558713.png?resizew=195)
(1)若队员射门训练时,射门角度
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6c96cb3ac8290e09c55d4eb336a8608.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/311ce164d7dc6f13f11b9a45989c09dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b702a991d4710fcb416a2436d87c99c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f687235bb361af7eb8f6bc37691d23ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
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5 . 已知曲线
,焦距长为
,右顶点A的横坐标为1.
上有一动点
,
和
关于
轴对称,直线
记为
,直线
为
,而且
,
与
轴的交点分别为
,
.
(1)求双曲线
的方程;
(2)已知以线段
为直径的圆过点
,且
为
轴上一点,求
的坐标;
(3)记S为三角形
的面积,当S取最小值时.求此时
点的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c5c2e64358e0ec7aa142c336d970306.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b91d650c2fc1a741fabdb333b09aeb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d89431ff6191fed25a4780b7e74d6876.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66a5b7813e902306477f91f9f4084cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c023f4b501684abd869b36d6e6c7f21f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知以线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(3)记S为三角形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/358cdecf669033e648c21dcf675df9b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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6 . 在平面直角坐标系
中:
①圆C过
和
,且圆心在直线
上;
②圆C过
三点.
(1)在①②两个条件中,任选一个条件求圆C的标准方程;
(2)在(1)的条件下,过直线
上的点
分别作圆C的两条切线
,
(Q,R为切点),求直线
的方程,并求弦长
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
①圆C过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c6ff81aedbefa935da289dc632e78eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e729a860cfd19d075a037b497bbfa04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3ce6e716f2a085b503b1ba7c8fc00cd.png)
②圆C过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3951c7f9b73330f7f29b4eae7306c9.png)
(1)在①②两个条件中,任选一个条件求圆C的标准方程;
(2)在(1)的条件下,过直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55aa0a20848c37c1892c567b2315e04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56e8da3e18d6d9d3ccd5974f2c187e44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/902f97913e1af1e6c793f7edfe6b2114.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d7b816eca15d4b7d060013df53edd53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ab59f50134d9bd1f2ad7e8dabcd5af9.png)
您最近一年使用:0次
名校
解题方法
7 . 已知圆
:
,
为圆
上任意一点,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c397129dacf0871ab2db37e60560f4b9.png)
(1)求
中点
的轨迹方程.
(2)若经过
的直线
与
的轨迹相交于
,在下列条件中选一个,求
的面积.
条件①:直线
斜率为
;②原点
到直线
的距离为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f5d967ad135991b6075ee45df55643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c397129dacf0871ab2db37e60560f4b9.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)若经过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2b83beedb3438153e6f728545fe3e03.png)
条件①:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afd3f14f202cd26f36711eefcdc03103.png)
您最近一年使用:0次
2023-02-22更新
|
245次组卷
|
3卷引用:江西省九校2022-2023学年高二下学期开学联考数学试题
8 . 已知点
和直线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d727778ea634df7c6607096bee39b0c8.png)
点
是点A关于直线
的对称点.
(1)求点
的坐标;
(2)
为坐标原点,且点
满足
.若点
的轨迹与直线
有公共点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee9c730266ecf448c14608e24d37b986.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d727778ea634df7c6607096bee39b0c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d3361eae6ffd24142f2e935dda5f552.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3a18adae759548edaa008e80fd29d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2023-02-14更新
|
636次组卷
|
4卷引用:湖北省咸宁市2022-2023学年高二上学期期末数学试题
名校
解题方法
9 . 已知
,
,
为
的三个顶点,圆Q为
的内切圆,点P在圆Q上运动.
(1)求圆Q的标准方程;
(2)求以
,
,
为直径的圆的面积之和的最大值、最小值;
(3)若
,
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cea6f63894aba70f5c4cfa7740eca6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ce7be37ff9418a9c95d5dc54814ebd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/872003897fb6163e4c8c710e3dadd7bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(1)求圆Q的标准方程;
(2)求以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d063ec7f9dbeba72fabf4437f9400e07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3ce8eed2660a33465a7f764e76cdba8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af4448a069a477b7a5a81a75d3469fc5.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1cf8af6e62058cc4e2d83d5da7f4c68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47c1d461a7491f49268983de8272b7a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa12542a1179dad4e734920f2a1c8c0c.png)
您最近一年使用:0次
2023-01-19更新
|
187次组卷
|
2卷引用:新疆乌鲁木齐市第101中学2022-2023学年高二下学期开学考试数学试题
名校
解题方法
10 . 党的二十大报告提出要加快建设交通强国.在我国
万平方千米的大地之下拥有超过
座,总长接近赤道长度的隧道(约
千米).这些隧道样式多种多样,它们或傍山而过,上方构筑顶棚形成“明洞”﹔或挂于峭壁,每隔一段开出“天窗”形成挂壁公路.但是更多时候它们都隐伏于山体之中,只露出窄窄的出入口洞门、佛山某学生学过圆的知识后受此启发,为山体隧道设计了一个圆弧形洞门样式,如图所示,路宽
为
米,洞门最高处距路面
米.
的方程.
(2)为使双向行驶的车辆更加安全,该同学进一步优化了设计方案,在路中间建立了
米宽的隔墙.某货车装满货物后整体呈长方体状,宽
米,高
米,则此货车能否通过该洞门?并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1139c55a2ab02b802c77bc0cb941befd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cca9545636580553121fe1d366c079bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e1ecb266000b2bf965f1cb03c18de88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c748e40ba21ac5063d3bccaa57ef278.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)为使双向行驶的车辆更加安全,该同学进一步优化了设计方案,在路中间建立了
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2023-01-11更新
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12卷引用:广东省佛山市2022-2023学年高二上学期期末数学试题
广东省佛山市2022-2023学年高二上学期期末数学试题第二章 直线和圆的方程 (单元测)(已下线)第09讲 2.5.1直线与圆的位置关系(2)黑龙江省牡丹江市第一高级中学2023-2024学年高二上学期10月月考数学试题广东省广州市第十六中学2023-2024学年高二上学期期中数学试题广东省东莞市七校2023-2024学年高二上学期期中联考数学试题广东省东莞市东莞实验中学2023-2024学年高二上学期第三次月考数学试题(已下线)2.5.1 直线与圆的位置关系 精练(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)(已下线)通关练11 圆的方程大题10考点精练(47题)- 【考点通关】2023-2024学年高二数学高频考点与解题策略(人教A版2019选择性必修第一册)吉林省延边第二中学2023-2024学年高二上学期第一次阶段检测数学试卷(已下线)第02讲 2.4圆的方程+2.5直线与圆,圆与圆的位置关系(4)(已下线)专题16 直线与圆的位置关系8种常见考法归类(3)