名校
解题方法
1 . 在平面直角坐标系中,定义
、
两点间的直角距离为
,如图,
是圆
当
时的一段弧,
是
与
轴的交点,将
依次以原点
为中心逆时针旋转
五次,得到由六段圆弧构成的曲线.则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de49f3cfe85c4ae1d7ecb30075848e87.png)
_______ .若点
为曲线上任一点,则
的最大值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d6f5adf13b4214666292dd64b947741.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af405a054bfe7fb7ce40e48d816467e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bea37e25ba5e11e5e2c428996f74e5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed41d321f4c0717ac5b443aad942d9a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/978ce4ca52b9c915574d50d64ce348b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/239ff12eb6cba0100f0dadb847c90ea8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed41d321f4c0717ac5b443aad942d9a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed41d321f4c0717ac5b443aad942d9a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de49f3cfe85c4ae1d7ecb30075848e87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4298f459599feb1a5ed4dce607b8e3d.png)
![](https://img.xkw.com/dksih/QBM/2021/5/8/2716842768228352/2718602291453952/STEM/3903e3564b0e40039bf873d70ad1e715.png?resizew=166)
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2021-05-11更新
|
983次组卷
|
5卷引用:湖北省武汉市第二中学2021-2022学年高三上学期暑期模拟数学试题
湖北省武汉市第二中学2021-2022学年高三上学期暑期模拟数学试题福建省南平市2021届高三二模数学试题(已下线)专题14 参数方程与极坐标方程-备战2022年高考数学(文)母题题源解密(全国乙卷)(已下线)专题27 直线与圆的综合应用-1北京市大兴区2023-2024学年高二上学期期中检测数学试题
解题方法
2 . 将参数方程为
(
为参数)化为普通方程为_______ .
![](https://img.xkw.com/dksih/QBM/2016/12/17/1619429694144512/1619429694423040/STEM/7e4a96c519ac4fbaaadf7dc32709a622.png?resizew=88)
![](https://img.xkw.com/dksih/QBM/2016/12/17/1619429694144512/1619429694423040/STEM/13f3748d5f3149a0950c319cb356f97b.png?resizew=9)
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3 . (选修4—4:坐标系与参数方程)
在直角坐标平面内,曲线
的参数方程为
(
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3d1a34ae2b8c77f8d7e355c6d1d667e.png)
为参数),以坐标原点
为极点,
轴的非负半轴为极轴建立极坐标系,已知点
、
的极坐标分别为
、
,若直线
和曲线C只有一个公共点,则
.
在直角坐标平面内,曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17274a351ce69eec64344e8c31cf08b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc855e49a30f27721021fe028f510575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3d1a34ae2b8c77f8d7e355c6d1d667e.png)
为参数),以坐标原点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://img.xkw.com/dksih/QBM/2015/10/8/1572244196278272/1572244202086400/STEM/16380b38663d4a5c95631655a3b6ac7d.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/8b673659ebf85260fee81b0ea10132ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfc903680b0320ebeacafc816f77a398.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/258e40e3883271c3580c1d3c805dcac6.png)
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4 . 已知曲线
的参数方程为
,若以坐标原点O为极点,
轴正半轴为极轴,曲线
的极坐标方程为
,那么C1上的点到曲线C2上的点的距离的最小值为 .
![](https://img.xkw.com/dksih/QBM/2015/6/19/1572132780638208/1572132786692096/STEM/f0999260297e4d7bb87ea673a423c3bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7889dafebece0a7add80a3117cb259d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://img.xkw.com/dksih/QBM/2015/6/19/1572132780638208/1572132786692096/STEM/631f4288d73142539584d480717d03c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b408d408f92357280db16452941f4ef.png)
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解题方法
5 . 曲线
,极坐标系(与直角坐标系xOy取相同的单位长度,以原点O为极点,x轴正半轴为极轴)中,直线
被曲线C截得的线段长为 .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/885cf1b728ba853e9da23fdb8462d541.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/705d2a7edc63e8ac461d179fefb30d07.png)
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6 . (选修4-4:坐标系与参数方程)在平面直角坐标系中,以坐标原点为极点,
轴的非负半轴为极轴建立极坐标系.已知直线
的参数方程为
(
为参数),圆
的极坐标方程为
.若圆
关于直线
对称,则
的值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f797ec6eb187bc94fe0b5467f6d82e7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5bc0942ce3f3d998b3335c5c9627096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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7 . 函数
的最大值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44dbca1916a5494270506a95b2e68bec.png)
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8 . (选修4-4:坐标系与参数方程)
在极坐标系中,点
到直线
的距离是________ .
在极坐标系中,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a50ce3b503db60ebec87b0395b1d4bda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e75e55220a698df3ea66aec60cff7f0.png)
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9 . 已知曲线
的参数方程是
(
为参数,a为实数常数),曲线
的参数方程是
(
为参数,b为实数常数).以坐标原点为极点,
轴的正半轴为极轴建立极坐标系,曲线
的极坐标方程是
. 若
与
分曲线
所成长度相等的四段弧,则![](https://img.xkw.com/dksih/QBM/2015/2/4/1571976991375360/1571976996741120/STEM/7c6bbc3000f5457b8c83cbe82b93ea64.png?resizew=63)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://img.xkw.com/dksih/QBM/2015/2/4/1571976991375360/1571976996741120/STEM/73c066eeb93d46449659323693cf9ad5.png?resizew=67)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://img.xkw.com/dksih/QBM/2015/2/4/1571976991375360/1571976996741120/STEM/2128367c76284efc96f3ee7f02a99bd4.png?resizew=20)
![](https://img.xkw.com/dksih/QBM/2015/2/4/1571976991375360/1571976996741120/STEM/b42fa5a930c84d9ab383e51f2a5ac4ff.png?resizew=76)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://img.xkw.com/dksih/QBM/2015/2/4/1571976991375360/1571976996741120/STEM/369ae93b7b434813aed693393a4ff82a.png?resizew=20)
![](https://img.xkw.com/dksih/QBM/2015/2/4/1571976991375360/1571976996741120/STEM/1b9b5a47c0194ad885e6fa05d1dbfd38.png?resizew=37)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://img.xkw.com/dksih/QBM/2015/2/4/1571976991375360/1571976996741120/STEM/369ae93b7b434813aed693393a4ff82a.png?resizew=20)
![](https://img.xkw.com/dksih/QBM/2015/2/4/1571976991375360/1571976996741120/STEM/7c6bbc3000f5457b8c83cbe82b93ea64.png?resizew=63)
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13-14高三·湖北·阶段练习
10 . (选修4-4:坐标系与参数方程)在极坐标系内,已知曲线C1的方程为
,以极点为原点,极轴方向为
正半轴方向,利用相同单位长度建立平面直角坐标系,曲线C2的参数方程为
(
为参数).设点P为曲线C2上的动点,过点P作曲线C1的两条切线,则这两条切线所成角余弦的最小值是_______ .
![](https://img.xkw.com/dksih/QBM/2014/12/16/1571924835311616/1571924841127936/STEM/9da82936f70444b0baf6f7ff7ee2b601.png?resizew=187)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://img.xkw.com/dksih/QBM/2014/12/16/1571924835311616/1571924841127936/STEM/2b41f1b1e8ad46e681dca3cb080e17c8.png?resizew=77)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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