名校
解题方法
1 . 在平面直角坐标系xOy中,已知直线l的方程为
,曲线C的参数方程为
(
为参数且
),以坐标原点O为极点,x轴的正半轴为极轴建立极坐标系.
(1)求曲线C的极坐标方程;
(2)若已知射线
,其中
且
与曲线C交于点M,与直线l交于点N,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66a325224b404376bcedc4129b56c173.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5806e9568f8c8ced0b6719ba6fb3a75d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f70b48360dc2b8c627bc4930dd509c0d.png)
(1)求曲线C的极坐标方程;
(2)若已知射线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dea7169b5c5de510de193d2b5dad5118.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a28bab4caf2c92e840962eb3a11459b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/309f416206e5f11c67408c3af0f9b4ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86971cee973445cfa3e853edf7ffba10.png)
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2022-01-15更新
|
1764次组卷
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6卷引用:贵州省贵阳市五校2022届高三11月联合考试数学(理)试题(三)
贵州省贵阳市五校2022届高三11月联合考试数学(理)试题(三)(已下线)数学-2022届高三下学期开学摸底考试卷C(理科)(新课标专用)(已下线)数学-2022届高三下学期开学摸底考试卷C(文科)(新课标专用)(已下线)必刷卷01 (理)-2022年高考数学考前信息必刷卷(全国乙卷)(已下线)必刷卷01(文)-2022年高考数学考前信息必刷卷(全国乙卷)四川省绵阳市三台中学校2024届高三下学期第二学月测试理科数学试题
名校
2 . 已知在平面直角坐标系
中,曲线
的参数方程为
(
为参数).以
为极点,
轴的非负半轴为极轴建立极坐标系,已知曲线
:
和
:
,曲线
分别交
,
于
,
两点.
(1)求曲线
的极坐标方程和曲线
的直角坐标方程;
(2)求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13b32361a0f172e79fe75959b1b2ab44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.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/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d931cd25c802877c3220b12662fd629.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab94459e87c666facddbe1a23ae1899d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1568a8676fbb3bf8ec868aad285b7ffc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab94459e87c666facddbe1a23ae1899d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1f0417d8269f01d8e0bc1a8756e2ac.png)
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2021-12-17更新
|
1255次组卷
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4卷引用:贵州省贵阳市第一中学2022届高三上学期高考适应性月考卷(三)数学(文)试题
名校
解题方法
3 . 在新中国成立70周年国庆阅兵庆典中,众多群众在脸上贴着一颗红心,以此表达对祖国的热爱之情.在数学中,有多种方程都可以表示心型曲线,其中有著名的笛卡尔心型曲线.如图,在直角坐标系中,以原点O为极点,x轴正半轴为极轴建立极坐标系.图中的曲线就是笛卡尔心型曲线,其极坐标方程为
,M为该曲线上的任意一点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/a032092a-3f11-4bbc-a62d-87bf35df53f7.png?resizew=157)
(1)当
时,求M点的极坐标:当M的极角为
时,求它的极径;
(2)若过极点的直线
与该曲线相交于两点A,B,求证:弦长
为定值,并求出这个定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad655f4f1fe74ae7f018fd0ef2711a36.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/a032092a-3f11-4bbc-a62d-87bf35df53f7.png?resizew=157)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a07205bc511042fdda781b84436fb157.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f99376e6b053ffd21b179108c18c3d3.png)
(2)若过极点的直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
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2021-07-24更新
|
840次组卷
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4卷引用:贵州省贵阳市第一中学2021届高三下学期高考适应性月考卷(五)数学(理)试题
贵州省贵阳市第一中学2021届高三下学期高考适应性月考卷(五)数学(理)试题贵州省贵阳市第一中学2021届高三下学期高考适应性月考卷(五)数学(文)试题(已下线)专题22 坐标系与参数方程-备战2022年高考数学(理)母题题源解密(全国甲卷)(已下线)专题22 坐标系与参数方程-备战2022年高考数学(文)母题题源解密(全国甲卷)
4 . 在平面直角坐标系
中,直线
的参数方程为
(其中
为参数).在以
为极点,
轴的非负半轴为极轴的极坐标系(两种坐标系的单位长度相同)中,曲线
的极坐标方程为
.
(1)求直线
的极坐标方程
(2)设直线
与曲线
交于
,
两点,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/303203a2393d1df7d12bec4352c67fed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfeaa2f79c85f28d15e8470de5a3ff03.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)设直线
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff24c95fe581befd56c3bcc70e88b726.png)
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2021-07-03更新
|
632次组卷
|
5卷引用:贵州省遵义市2022届高三上学期第一次质量监测数学(文)试题
名校
解题方法
5 . 直角坐标系
中,以坐标原点为极点,以
轴正半轴为极轴,建立极坐标系,曲线
的极坐标方程为
.
(1)曲线
与直线
:
交于
,
两点,求
;
(2)曲线
的参数方程为
(
,
为参数),当
时,若
与
有两个交点,极坐标分别为
,
,求
的取值范围,并证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a96024cf288b721471537d2c8e45790f.png)
(1)曲线
![](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/35c7afba7fa24b295454141892a5a986.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/3f4dfec890cdfdda355e19463f3be813.png)
(2)曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a709b826b06d39133fbdc3943a726483.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45ba6b6aa6c3f9faba6b03bc193a6e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6eec7d75a66a4407631f75320bb8b15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ae7970f9d4bf5cbb2931aea0895927d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/122c6f6224e7cb567cde925dd7484935.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b17d334659e2ec80210dd2889c6ba74.png)
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2021-05-05更新
|
594次组卷
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4卷引用:贵州省普通高等学校招生2021届高三适应性测试(3月)数学(理)试题
名校
6 . 如图是美丽的三叶草图案,在以
为极点,
轴为极轴的极坐标系中,它由弧
,弧
,弧
组成.已知它们分别是方程为
,
,
的圆上的一部分.
![](https://img.xkw.com/dksih/QBM/2021/3/19/2681348457955328/2685373738180608/STEM/8a1a733d6caa4bc398bef55731d26800.png?resizew=202)
(1)分别写出点
的极坐标;
(2)设点
是由点
所确定的圆
上的动点,直线
,求点
到
的距离的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3e5af20b2f8c1fba4470f9650989e51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/624fb161f585a924416360c41ec75897.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ae728c7be0f0cf78711f3fa5ccccf30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6359e4d0b0d8b541e9ed09e59a653e18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e73f8bf07a0a9d3ca809cbdb9fdf2e70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb3d2c3e4fe6f157778c282d0306655c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9514468ce4ea82166ffd713a4b0743c0.png)
![](https://img.xkw.com/dksih/QBM/2021/3/19/2681348457955328/2685373738180608/STEM/8a1a733d6caa4bc398bef55731d26800.png?resizew=202)
(1)分别写出点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e96c92bc20565fb976e0c73ee4017261.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e96c92bc20565fb976e0c73ee4017261.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcb05889e92989580ff29540bf922568.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
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2021-03-25更新
|
548次组卷
|
3卷引用:贵州省遵义市2021届高三第一次模拟数学(理)试题
名校
7 . 第三届中国国际进口博览会的建筑主体为“四叶草”造型,“四叶草”是绿色的有生命力的象征,其优美的曲线与江南地区海派文化的优雅唯美气质相应和,表达了中国对未来经济持续发展、人民生活富裕的美好向往;“四叶草”作为世界通用的吉祥图形,四瓣叶子分别寓意着“至爱、健康、荣誉、富裕”,整体带有吉祥、和谐的意义如图,在极坐标系
中,方程
表示的图形为“四叶草”对应的曲线
.
![](https://img.xkw.com/dksih/QBM/2021/1/23/2642464959455232/2645184517480448/STEM/035f3232b05142e1aa6e833bc6c07a9d.png?resizew=281)
(1)设直线
与
交于异于
的两点
,
,求
、
两点的极坐标;
(2)设
、
是
上异于
的两点,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3e5af20b2f8c1fba4470f9650989e51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f8f685b56af9fc76e315da7c3e6cc16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://img.xkw.com/dksih/QBM/2021/1/23/2642464959455232/2645184517480448/STEM/035f3232b05142e1aa6e833bc6c07a9d.png?resizew=281)
(1)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b40fda49a8cf8e67d69014a8ed36099b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)设
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/084cf5ffced059f5653ee2a1023518b7.png)
您最近一年使用:0次
2021-01-27更新
|
347次组卷
|
2卷引用:贵州省盘州市2021届高三第一学期第一次模拟考试理科数学试题
8 . 在平面直角坐标系
中,圆
的参数方程为
(
为参数),直线
的参数方程为
(
为参数),设原点
在圆
的内部,直线
与圆
交于
、
两点;以坐标原点
为极点,
轴的正半轴为极轴建立极坐标系.
(1)求直线
和圆
的极坐标方程,并求
的取值范围;
(2)求证:
为定值.
![](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/f6c4a027310e2afbc715fb5ec6cea33f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8b8876c9b971d4a16429a9019ca9ba2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)求直线
![](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/0a6936d370d6a238a608ca56f87198de.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fffd2e3363992060c0b8785f031d2877.png)
您最近一年使用:0次
2020-05-30更新
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954次组卷
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8卷引用:贵州省贵阳为明教育集团2021届高三第一次调研理科数学试题
名校
解题方法
9 . 在新中国成立70周年国庆阅兵庆典中,众多群众在脸上贴着一颗红心,以此表达对祖国的热爱之情,在数学中,有多种方程都可以表示心型曲线,其中有著名的笛卡尔心型曲线,如图,在直角坐标系中,以原点O为极点,x轴正半轴为极轴建立极坐标系.图中的曲线就是笛卡尔心型曲线,其极坐标方程为
(
),M为该曲线上的任意一点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/1/7e93ee35-4089-43e3-84a0-83c3f2b1d78d.png?resizew=260)
(1)当
时,求M点的极坐标;
(2)将射线OM绕原点O逆时针旋转
与该曲线相交于点N,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d48085c5aa3deb1fbdfa812daee0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64bd03b70d08194b216461ca115f00d4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/1/7e93ee35-4089-43e3-84a0-83c3f2b1d78d.png?resizew=260)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/441e9aa011d5f42f3b292b507bb9d3b8.png)
(2)将射线OM绕原点O逆时针旋转
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ad72d7565699d1ebb741eb0ce12bac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/084cf5ffced059f5653ee2a1023518b7.png)
您最近一年使用:0次
2020-03-23更新
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1244次组卷
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21卷引用:贵州省安顺市2021届全市高三年级第一次教学质量监测统一考试数学(理)试题
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