1 . 在直角坐标系
中,已知曲线
的参数方程为
(
为参数).
(1)写出曲线
的普通方程;
(2)设
为曲线
上的一点,将
绕原点
顺时针旋转
得到
.当
运动时,设点
的轨迹是
,求曲线
的直角坐标方程.
![](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/7ebe6d0c8372c3f4cf143fa01a5f9d41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(1)写出曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](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/91174b2336306191ba275a87864172b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4731335d26e45bf7041b36c5f0a1121d.png)
![](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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
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2024-03-07更新
|
661次组卷
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4卷引用:内蒙古赤峰市2023~2024学年高三上学期1.30模拟文科数学试题
2 . 在直角坐标系
中,曲线
的参数方程为
为参数
,
(1)写出
的普通方程,并指出它是什么曲线;
(2)以坐标原点为极点,
轴正半轴为极轴建立极坐标系,曲线
的极坐标方程为
,求
与
交点的极径与极角的正切值.
![](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/bed4e17e355f848096537fdb408eae34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
(1)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)以坐标原点为极点,
![](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/ab9d5a620b1214d121cd4d9c3654d1f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
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4卷引用:内蒙古自治区锡林郭勒盟2023-2024学年高三上学期1月期末教学质量检测理科数学试题
解题方法
3 . 在直角坐标系
中,曲线
的参数方程为
(
),曲线
的参数方程为
(
为参数).
(1)求曲线
的普通方程;
(2)若
,
,在曲线
上任取一点
,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/0a36ff195cedc3d2903e1694bb6e1379.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c1592e2f4c18943d1c5321959d1801f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bce5c1ab2f15c357ea56379faa950ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383f12cb70ca55eba4ff012771dbfa9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/513eafd10fa1ec0196562865517e0b09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
您最近一年使用:0次
2024-01-24更新
|
205次组卷
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2卷引用:内蒙古呼和浩特市2024届高三上学期学业质量监测数学(文)试题
4 . 在平面直角坐标系
中,曲线
的参数方程为
(
为参数).以
为极点,
轴的正半轴为极轴建立极坐标系,曲线
的极坐标方程为
.
(1)求曲线
的普通方程与曲线
的直角坐标方程;
(2)已知点
的直角坐标为
,曲线
与曲线
交于
、
两点,求
的值.
![](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/1d3a50bb451bc161765aea572237d279.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.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/20b54bf219a714343bdbb721ef0406e5.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbfc36eb774c5856383f01bfa06e9dd6.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a104774601235cc76b5f0c1683c974e1.png)
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2023-11-29更新
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2卷引用:内蒙古自治区赤峰市第四中学2024届高三上学期期中数学(文)试题
名校
5 . 在平面直角坐标系
中,射线l的方程为
,曲线C的方程为
.以坐标原点为极点,x轴非负半轴为极轴建立极坐标系.
(1)求射线l和曲线C的极坐标方程;
(2)若射线l与曲线C交于点P,将射线
绕极点按逆时针方向旋转
交C于点Q,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cfb764b285362ee742b6dc613a1460a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c82e7d9f4f7ace849e09e9adcb786b7f.png)
(1)求射线l和曲线C的极坐标方程;
(2)若射线l与曲线C交于点P,将射线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d49f8a63ddbca52039fa9ab44cda6b29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fdc02f00cf00a6dfd88b53a90f1f7a4.png)
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2023-11-27更新
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7卷引用:内蒙古鄂尔多斯市西四旗2024届高三上学期期末综合模拟数学(理)试题
2023·全国·模拟预测
6 . 在直角坐标系xOy中,曲线C的参数方程为
(t为参数).以坐标原点O为极点,x轴正半轴为极轴建立极坐标系,直线l的极坐标方程为
.
(1)求曲线C的普通方程和直线l的直角坐标方程;
(2)过点
作直线l的平行线交曲线C于M,N两点(M在x轴上方),求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f63baf9406aa2d99e6f623d6c6c78511.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13f7d6b2654c7980b29053d513405891.png)
(1)求曲线C的普通方程和直线l的直角坐标方程;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7607c37caa9d8616fe17b154adcb727c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4302b8e9f76aca8454d3df72e80be2bc.png)
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2023-11-22更新
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3卷引用:内蒙古自治区通辽市科尔沁左翼中旗实验高级中学2024届高三上学期12月月考数学(文)试题
内蒙古自治区通辽市科尔沁左翼中旗实验高级中学2024届高三上学期12月月考数学(文)试题(已下线)2024年普通高等学校招生全国统一考试理科数学领航卷(二)四川省绵阳市南山中学实验学校2024届高考补习年级二诊模拟数学试题(四)
2023·全国·模拟预测
7 . 在平面直角坐标系
中,圆
.以坐标原点
为极点,
轴正半轴为极轴建立极坐标系,圆
的极坐标方程为
.
(1)判断圆
与圆
的位置关系;
(2)若直线
的极坐标方程为
,直线
与
轴交于点
,与圆
交于
两点,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a600390189fea63fde543a6d64a8a59d.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/6cafb579dd4af3a4b9d38e747f5cd9e7.png)
(1)判断圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/381c69568330e44bfb81040753fedfdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d05973a156ca66661253a02537dd303d.png)
您最近一年使用:0次
名校
8 . 在平面直角坐标系
中,曲线
的参数方程为
(其中
为参数),以坐标原点
为极点,
轴的正半轴为极轴建立极坐标系,直线
的极坐标方程为
,点
的极坐标为
.
(1)求直线
的直角坐标方程与曲线
的普通方程;
(2)若
是曲线
上的动点,
为线段
的中点,求点
到直线
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/e8168bdaa1821c667d8c42002f753f32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7058ca92334714eef90d8586fcaadd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fd54856458cc63cd71ae76230a5b635.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2023-11-15更新
|
606次组卷
|
3卷引用:内蒙古赤峰市赤峰二中2024届高三上学期12月月考数学(理)试题
9 . 在平面直角坐标系中,曲线
,曲线
的参数方程为
(
为参数).以坐标原点
为极点,
轴的正半轴为极轴建立极坐标系.
(1)求曲线
的极坐标方程;
(2)在极坐标系中,射线
与曲线
分别交于
两点(异于极点
),求
的长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/507cfb48a961b46345c1436256484756.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c70b43d6b9b8235cabe70895fb934a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9feabc99f62ee569b460e61526e2e.png)
(2)在极坐标系中,射线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a40d2cf43fce0c99dff3470d554eb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9feabc99f62ee569b460e61526e2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
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2023-11-03更新
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472次组卷
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3卷引用:内蒙古蒙东七校2024届高三上学期11月联考数学(文)试题
10 . 在平面直角坐标系
中,曲线C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:
(
,
),已知直线l与曲线C相交于M,N两点.
(1)求曲线C的极坐标方程;
(2)记线段
的中点为P,若
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2959ac15d5f3a791f94ab9aa19a0d3fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.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/6be32a39d99bbd36fff0d12a2708d268.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8472d44b3ce886705208978a95e5fcc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f614267fccee84d04f69d6831434a008.png)
(1)求曲线C的极坐标方程;
(2)记线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7886b17f9f470bf7f1fcbb40206e8a.png)
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