名校
1 . 在直角坐标系
中,已知曲线
(
为参数),在极坐标系中,曲线
是以
为圆心且过极点
的圆.
(1)分别写出曲线
普通方程和曲线
的极坐标方程;
(2)直线
与曲线
、
分别交于
、
两点(异于极点
),求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a28ccba5981ff469c05f7fcc48897474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97e967ff5c1c3bc20a29e3cfce1e374.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(1)分别写出曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efbf5c22e89f0b2c1a93dbb2bf3eb015.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/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/084cf5ffced059f5653ee2a1023518b7.png)
您最近一年使用:0次
2023-08-03更新
|
270次组卷
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7卷引用:广西玉林市北流市2023届高三年级教学质量检测数学(理)试题
2 . 曲线
的参数方程为:
,
为参数.以原点为极点,
轴正半轴为极轴建立极坐标系,直线
的方程为
.
(1)求曲线
的普通方程和极坐标方程.
(2)若直线
与曲线
相交于点A,点B在圆
:
上,求
的最小值及此时的
值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/040c52750f7133583850305ee063b471.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](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/17f5d2e8186f0173d7862b1d39fb3dc2.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63b8e68713c34c549d9b841d35322eca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
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名校
3 . 在直角坐标系xOy中,曲线
的参数方程为
(t为参数且
),
分别与x轴、y轴交于A、B两点.以坐标原点O为极点,x轴的非负半轴为极轴建立极坐标系,曲线
的极坐标方程为
.
(1)
与坐标轴交于A,B两点,求
;
(2)求
上的点到直线AB距离的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e8751d60072368150728b384aa48ce6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a369ce3949b2bd2747a48054f7b951c4.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/9b4c7a1116fa778512168b6b5b99ae24.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
您最近一年使用:0次
2023-05-12更新
|
762次组卷
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2卷引用:广西南宁市第三中学2023届高三一模测试数学(理)试题
4 . 在平面直角坐标系
中,圆
的方程为
.以坐标原点为极点,
轴的正半轴为极轴建立极坐标系.
(1)求圆
的极坐标方程;
(2)若射线
(
,
)与圆
交于
,
两点,且
,求直线
的直角坐标方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb96e1b322d79d5dae24b988d2b4e981.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)若射线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17f5d2e8186f0173d7862b1d39fb3dc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bc282dae4ac9132196ac5d13f63b901.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7026315511e1afd55a97b5278b0dd2cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.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/4a4b3b42d4a98693fa12f0cc3a095d02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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2023-05-07更新
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2卷引用:广西桂林市、北海市2023届高三联合模拟考试数学(文)试题
解题方法
5 . 已知曲线
的参数方程是
(
是参数),以坐标原点为极点,
轴的非负半轴为极轴建立极坐标系.
(1)写出曲线
的极坐标方程;
(2)若点
,
,
在曲线
上,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13ddb104406e14773c9cc60bda30c91b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)写出曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/299e193c0bb7580f2e0a6f122634f098.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc05578fbe4e91c91900dea4c50f5f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05211187f61de40869dd0c5b0b5e9c4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0f353bf37e83b723b3b74821feb91db.png)
您最近一年使用:0次
2023-05-03更新
|
121次组卷
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2卷引用:广西邕衡金卷2023届高三一轮复习诊断性联考数学(理)试题
6 . 在平面直角坐标系
中,已知曲线
(
为参数),直线
(t为参数),以坐标原点为极点,x轴的正半轴为极轴建立极坐标系.
(1)求曲线C和直线l的极坐标方程;
(2)点P在直线l上,射线
交曲线C于点R,点Q在射线
上,且满足
,求点Q的轨迹的直角坐标方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c1f0b45917ffd29c617fb327ee53010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bd891960819ffe8fb6794c240ece545.png)
(1)求曲线C和直线l的极坐标方程;
(2)点P在直线l上,射线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e68b0e37044602ad9d6011bfce9f077a.png)
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2023-04-20更新
|
684次组卷
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6卷引用:广西南宁市2023届高三二模数学(理)试题
广西南宁市2023届高三二模数学(理)试题广西南宁市2023届高三二模数学(文)试题(已下线)专题20坐标系与参数方程(已下线)专题20坐标系与参数方程.(已下线)2024年全国高考名校名师联席命制数学(理)信息卷(十)(已下线)2024年全国高考名校名师联席命制数学(文)信息卷(十)
7 . 在直角坐标系
中,曲线
的参数方程为
(
为参数),以坐标原点为极点,
轴正半轴为极轴建立极坐标系,直线
的极坐标方程为
.
(1)求曲线
的普通方程与直线
的直角坐标方程;
(2)设
、
分别为曲线
和直线
上的任意一点,求
的最小值.
![](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/cea9a8ef5e0327f2d062ca5a49d3dcea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](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/df410d824214f11a11fba4cae0dbc704.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d44e8bc37ed03f44470762748a8f942a.png)
您最近一年使用:0次
2023-04-18更新
|
637次组卷
|
3卷引用:广西壮族自治区南宁市第三中学2023届高三模拟数学(理)试题(一)
名校
解题方法
8 . 杭州2022年第19届亚运会(The 19th Asian Games Hangzhou 2022),简称“杭州2022年亚运会”,将在中国浙江杭州举行,原定于2022年9月10日至25日举办;2022年7月19日亚洲奥林匹克理事会宣布将于2023年9月23日至10月8日举办,赛事名称和标识保持不变。某高中体育爱好者为纪念在我国举办的第三次亚运会,借四叶草具有幸福幸运的象征意义,准备设计一枚四叶草徽章捐献给亚运会。如图,在极坐标系Ox中,方程
表示的图形为“四叶草”对应的曲线C.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/16/fcd7540b-4d08-426f-8d38-c9b1f3aec7aa.png?resizew=166)
(1)设直线l:
与C交于异于O的两点A、B,求线段AB的长;
(2)设P和Q是C上的两点,且
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d46f514e6bb42182699a0984eac19e81.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/16/fcd7540b-4d08-426f-8d38-c9b1f3aec7aa.png?resizew=166)
(1)设直线l:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b4834227ae67d63cf11c6b7cd62a98b.png)
(2)设P和Q是C上的两点,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10a3d200ed5c85cda5b72318db65d4bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb5e43e026ddf27fa210372532abb8d6.png)
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2023-04-14更新
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2203次组卷
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8卷引用:广西梧州市苍梧中学2023届高三5月份高考数学模拟试题
名校
9 . 在直角坐标系
中,曲线
的普通方程为
:
,曲线
的极坐标方程为:
,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
参数方程和曲线
的普通方程;
(2)若曲线
与曲线
,
分别交于M,N两点,求
.
![](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/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf6dba18751d6641f9fa02f5756be97a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbc53e1dbc3b6560d78e59400e4613ff.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad8602f27b106a049be2d925304bd70e.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/084cf5ffced059f5653ee2a1023518b7.png)
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2023-04-13更新
|
656次组卷
|
2卷引用:广西柳州高级中学、南宁市第三中学2023届高三联考数学(文)试题
名校
10 . 在平面直角坐标
中,曲线C的参数方程为
(
为参数),以原点O为极点,x轴的正半轴为极轴建立极坐标系,直线
的极坐标方程为
.
(1)写出曲线
的普通方程;
(2)若
与
有公共点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd8cc57651d8e96dd7344e0cdcbe2e90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39c7940cba997159d67aff9383028037.png)
(1)写出曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](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/294f5ba74cdf695fc9a8a8e52f421328.png)
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2023-04-09更新
|
1107次组卷
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7卷引用:广西桂林市、崇左市2023届高三一模数学(理)试题