1 . 在直角坐标系中,曲线
的参数方程为
.以坐标原点为极点,
轴的正半轴为极轴的极坐标系中.曲线
的极坐标方程为
.
(1)分别把曲线
化成普通方程和直角坐标方程;并说明它们分别表示什么曲线.
(2)在曲线
上求一点
,使点
到曲线
的距离最小,并求出最小距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1bc0705cb345cab679c8aeaf30e9d77.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/95079808882eec6af135e8a5ddfbd546.png)
(1)分别把曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eac675dac08c4b88fb66fccda568fa9.png)
(2)在曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
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名校
2 .
在直角坐标系
中,以坐标原点
为极点,
轴的正半轴为极轴建立极坐标系,已知曲线
的极坐标方程为
.
(1)求曲线
的直角坐标方程;
(2)若直线
与直线
(
为参数,
)交于点
,与曲线
交于点
(异于极点),且
,求
.
在直角坐标系
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.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/00999b9a5320bad39b04ad762aa71a0a.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/bca596f1dd6d7eefb04821eccf2934de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/244e242443f7efcb72eb792da8e85faa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fa8e35f8c1731c9563bab260380170e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2018-06-20更新
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838次组卷
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5卷引用:黑龙江省大庆市大庆实验中学2020-2021学年高二下学期开学考试文科数学试题
名校
3 . [选修4-4:坐标系与参数方程]
以坐标原点
为极点,
轴的正半轴为极轴建立极坐标系,已知曲线
的极坐标方程为
.
(1)写出曲线
的参数方程;
(2)在曲线
上任取一点
,过点
作
轴,
轴的垂直,垂足分别为
,
,求矩形
的面积的最大值.
以坐标原点
![](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/f763f33c602106908f4e63da5e9f4dcb.png)
(1)写出曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)在曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.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/14e902eb263971b466d0fcd91c56b453.png)
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2018-06-09更新
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6卷引用:2020届黑龙江省大庆实验中学高三下学期复习考试数学(理)试题
4 . 在直角坐标系
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
,点
的曲线
上运动.
(1)若点
在射线
上,且
,求点
的轨迹的直角坐标方程;
(2)设
,求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.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/4c25a8e983a47bcbd88ecdcee332f408.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12c53cf120cd5c7bbcdade68e75d57c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5934c425e35860667320f5f4cc8422d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c0da03ec477a5e17b7f4de370638024.png)
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5 . 在直角坐标系
中,以坐标原点
为极点,以
轴正半轴为极轴,建立极坐标系,圆
的方程为
,直线
的极坐标方程为
.
(Ⅰ)写出
的极坐标方程和
的平面直角坐标方程;
(Ⅱ)若直线
的极坐标方程为
,设
与
的交点为
与
的交点为
求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7795aec93c2c7ac2fd93e6747ca6516c.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/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2797374b0c4fa969fd6e41e596c9d958.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f72d83fb67aadcde0712e30437b1b50c.png)
(Ⅰ)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(Ⅱ)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab94459e87c666facddbe1a23ae1899d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3ec9d3c72965671aa75c537e6a4740b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12ba96c553da7be759d8095fa7c495a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24f23dcb213b47acf215cc87d5b5254c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dd698d57d1cf239eb8752aecaaa4f4.png)
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2018-04-24更新
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2卷引用:黑龙江省大庆市2018届高三第二次教学质量检测理科数学试题
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6 . 已知曲线C的参数方程为
(α为参数),以直角坐标系的原点O为极点,x轴正半轴为极轴建立极坐标系.
(1)求曲线C的极坐标方程;
(2)设l1:
,l2:
,若l1,l2与曲线C相交于异于原点的两点A,B,求△AOB的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b71ba5b4348e86c308c26a6ed10f564e.png)
(1)求曲线C的极坐标方程;
(2)设l1:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/734a6a1d319648bb969845a9159cdba7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bc1f08c7640e62e8717abf4d44a6c83.png)
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2017-09-21更新
|
576次组卷
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5卷引用:黑龙江省哈尔滨市第六中学2020-2021学年高二下学期开学考试数学(理)试题
名校
7 . 选修4—4:坐标系与参数方程
在直角坐标系
中,以坐标原点O为极点,
轴正半轴为极轴建立极坐标系,曲线
,曲线
.
(Ⅰ)求曲线
的一个参数方程;
(Ⅱ)若曲线
和曲线
相交于A、B两点,求
的值.
在直角坐标系
![](https://img.xkw.com/dksih/QBM/2017/5/27/1695796677656576/1701573058691072/STEM/23c1c02414294f2b8e20d84ba1a39ba8.png?resizew=29)
![](https://img.xkw.com/dksih/QBM/2017/5/27/1695796677656576/1701573058691072/STEM/61683207d1814305835f12f6e7903b33.png?resizew=12)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63632935400844396c37af26082c4ec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad4fc94ec96275e3a00a4ad88fd50502.png)
(Ⅰ)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(Ⅱ)若曲线
![](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/05da40a2d7dab5d6a003906ca19d4749.png)
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2017-06-05更新
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7卷引用:【全国省级联考】黑龙江省2018届高三普通高等学校招生全国统一考试 仿真模拟(五)数学试题(理科)
名校
8 . 以平面直角坐标系的坐标原点
为极点,以
轴的非负半轴为极轴,以平面直角坐标系的长度为长度单位建立极坐标系. 已知直线
的参数方程为
(
为参数),曲线
的极坐标方程为
.
(1)求曲线
的直角坐标方程;
(2)设直线
与曲线
相交于
两点,求
.
![](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/bca5bd0666df74a3de1116263085c107.png)
![](https://img.xkw.com/dksih/QBM/2017/5/25/1694690930204672/1701734595223552/STEM/06772090c5c54f7db05bb9b37554c374.png?resizew=9)
![](https://img.xkw.com/dksih/QBM/2017/5/25/1694690930204672/1701734595223552/STEM/212253743d4c41529c4db5b820759c97.png?resizew=16)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00999b9a5320bad39b04ad762aa71a0a.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设直线
![](https://img.xkw.com/dksih/QBM/2017/5/25/1694690930204672/1701734595223552/STEM/3bcc4e2fb2d440febbf687ad6f5d094f.png?resizew=9)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05da40a2d7dab5d6a003906ca19d4749.png)
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2017-06-04更新
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14卷引用:黑龙江省鹤岗市第一中学2019-2020学年高三上学期10月月考数学(文)试题
黑龙江省鹤岗市第一中学2019-2020学年高三上学期10月月考数学(文)试题陕西省黄陵中学2017届高三(重点班)下学期高考前模拟(一)数学(理)试题陕西省西安市八校2018届高三上学期第一次联考数学(文)试题陕西省西安市八校2018届高三上学期第一次联考数学(理)试题(已下线)《高频考点解密》—解密30 坐标系与参数方程(已下线)解密26 坐标系与参数方程-备战2018年高考文科数学之高频考点解密【全国百强校】山东省潍坊市寿光现代中学2017-2018学年高二6月月考数学(理)试题河南省郑州市第一中学2018-2019学年高二下学期期中考试文科数学试题2020届陕西省榆林市高三模拟第一次测试文数试题2020届陕西省榆林市高三模拟第一次测试理数试题河北省承德第一中学2020届高三下学期3月线上考试数学(文)试题(已下线)解密23 坐标系与参数方程 (讲义)-【高频考点解密】2021年高考数学(理)二轮复习讲义+分层训练(已下线)解密21 坐标系与参数方程 (讲义)-【高频考点解密】2021年高考数学(文)二轮复习讲义+分层训练甘肃省兰州市第二中学2021-2022学年高三上学期线上考试(理科)数学试题
名校
9 . 选修4-4:坐标系与参数方程
在平面直角坐标系
中,将圆
:
上每一个点的横坐标不变,纵坐标变为原来的
,得到曲线
.
(1)求曲线
的参数方程;
(2)以坐标原点
为极点,以
轴非负半轴为极轴建立极坐标系,在两坐标系中取相同的单位长度,射线
与圆
和曲线
分别交于点
,求
的最大值.
在平面直角坐标系
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f5d967ad135991b6075ee45df55643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)以坐标原点
![](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/e1c378ecb685d21c258b5f7b47e332fd.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaff41080fdea43eea7efedf9ebc1498.png)
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2017-06-03更新
|
713次组卷
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2卷引用:黑龙江省哈尔滨市第三中学2017届高三四模文科数学试题
名校
10 . 选修4-4:坐标系与参数方程
在平面直角坐标系
中,斜率为1的直线
过定点
.以
为极点,
轴的非负半轴为极轴建立极坐标系.已知曲线
的极坐标方程为
.
(1)求曲线
的直角坐标方程以及直线
的参数方程;
(2)两曲线相交于
两点,若
,求
的值.
在平面直角坐标系
![](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/2a84ce047387d00e506351deb1e35d7c.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/1bddf0b3db29426b5f1c396736b7f667.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)两曲线相交于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88659e1bac79840020d4494440cfb8e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7f618c20607afa7c345e81d33878148.png)
您最近一年使用:0次
2017-03-30更新
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1146次组卷
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6卷引用:黑龙江省哈尔滨市双城区兆麟中学2019-2020学年高二下学期期末考试数学(文)试题