1 . 赵州桥是世界上现存年代最久远,跨度最大,保存最完整的单孔坦弧敞肩石拱桥.赵州桥的设计应用到平摆线:当一个圆沿着一条直线作无滑动的滚动时,圆周上的定点
的轨迹为平摆线.赵州桥的拱可以近似看作平摆线,设拱与水面交于
,
两点(
在
的左侧),
,若拱左半部分的一点
到水面的距离为
,则线段
长度的近似值为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/27/224cfc9a-10d0-42dd-ab0a-4bb127475e01.png?resizew=196)
![](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/54a5d7d3b6b63fe5c24c3907b7a8eaa3.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/e4ec4a9575f77fb1fead46c1f930edf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e17ee14bd91bfff409c06fd434f6745.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30f954a8da05cc9144d4bf86f88e236a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/27/224cfc9a-10d0-42dd-ab0a-4bb127475e01.png?resizew=196)
A.![]() | B.![]() | C.![]() | D.![]() |
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2023·江西·二模
2 . 研究某点轨迹时,数学上常用向量来表示一个点.例如:M是车轮边缘的一点,初始态在原点,车轮半径为r,轮子沿着x轴滚动,M点的轨迹
即为摆线
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/12/69603ab5-65af-44a5-9dbb-1939222d5bc4.png?resizew=340)
(1)若以车轮旋转角度为参数,请写出M轨迹的参数方程
(2)若坐标原点处固定一半径为r的轨道,现在让车轮沿着该轨道转一圈,M初始态在
点,试写出M轨迹的参数方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82a79a33a83a7ba57a34b5093d1d1d02.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/12/69603ab5-65af-44a5-9dbb-1939222d5bc4.png?resizew=340)
(1)若以车轮旋转角度为参数,请写出M轨迹的参数方程
(2)若坐标原点处固定一半径为r的轨道,现在让车轮沿着该轨道转一圈,M初始态在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411a2b535a9a2fd094c4f19c2698b60b.png)
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名校
3 . 当一个圆沿着一条定直线无滑动地滚动时,圆周上一个定点的轨迹是摆线.在直角坐标系
中,摆线
的参数方程为
(
为参数,且
).
(1)求
上的点到
轴的距离的最大值;
(2)求
上的点到原点的距离的最大值.
![](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/b0dd3046050c72cc430e4934d8c7a843.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5dbd8f2e566d5aec0284562c03dc0ef1.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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2022-05-02更新
|
382次组卷
|
4卷引用:云南省昆明市第一中学2022届高三第九次考前适应性训练数学(理)试题
云南省昆明市第一中学2022届高三第九次考前适应性训练数学(理)试题云南省昆明市第一中学2022届高三第九次考前适应性训练数学(文)试题(已下线)押全国卷(文科)第22题 坐标系与参数方程-备战2022年高考数学(文)临考题号押题(全国卷)(已下线)文科数学-2022年高考考前20天终极冲刺攻略(四)(6月3日)
4 . 圆的摆线上有一点
,在满足条件的所有摆线的参数方程中,使圆的半径最大的摆线上,参数
对应的点的坐标为________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8297b9e5a6a3e96fef87a4125ca9ebcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/804fb6b691ed417751d1348a0e2d02a1.png)
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5 . 如图所示,圆的渐开线的基圆的半径为
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/26/e9e8e56a-1938-4fca-967e-111598b6e088.png?resizew=158)
(1)写出圆的渐开线的参数方程;
(2)求
对应的渐开线上的点
与切点
之间的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ce9433909d7423bcb7a2a8dbc410790.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/26/e9e8e56a-1938-4fca-967e-111598b6e088.png?resizew=158)
(1)写出圆的渐开线的参数方程;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d7b2fe01a33c4825f9974ed9663a99c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
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6 . 摆线
(
为参数,
)与直线
的交点的直角坐标是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c3007820673ea8d6c54638ee2012c5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f52f077d2eed7ebe17d1574c045662a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/107babba45f110012183dc4dc54490f7.png)
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
您最近一年使用:0次
2019-07-04更新
|
190次组卷
|
2卷引用:人教A版 全能练习 选修4-4 第二讲 第四章 1.渐开线2.摆线
名校
7 . 已知圆的渐开线的参数方程为
,(
为参数),则此渐开线的基圆的周长是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17584b0ee05db7c9f531a44132e3617f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2019-07-04更新
|
180次组卷
|
2卷引用:人教A版 全能练习 选修4-4 第二讲 第四章 1.渐开线2.摆线
8 . 已知圆的参数方程为
(
为参数),直线
.
(1)如果把圆心平移到原点
,请问平移后圆和直线满足什么关系?
(2)写出平移后圆的摆线方程.
(3)求摆线和
轴的交点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a59cfc2a59f4c6ca165b37fa56b93aea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8e5145a0824dd84e04c182aac3eb25c.png)
(1)如果把圆心平移到原点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(2)写出平移后圆的摆线方程.
(3)求摆线和
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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9 . 如图所示,点
在圆
的半径
上(或在半径
的延长线上),当圆
沿
轴正方向滚动时,称点
的轨迹为变幅平摆线.若圆
上点
的初始位置
为坐标原点,取
或
,请推出点
的轨迹的参数方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13b080797a80c606da7fcc3a75f15041.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d6873c800906bc0bc9542592b3246f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/20/31eacbca-62a9-4428-9e57-1e3a68ac63a4.png?resizew=169)
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10 . 圆的渐开线
(
为参数)上与
对应的点的直角坐标为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/659558c5e9334e2fd79ee9d953eb8c0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10c2ee2c29562dccadc42f2121ef8642.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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