1 . 在直角坐标系
中,直线
的参数方程为
(
为参数),在以坐标原点为极点,
轴正半轴为极轴的极坐标系中,曲线
的方程为
.
(1)求曲线
的直角坐标方程;
(2)设曲线
与直线
交于点
,点
的坐标为
,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/4f9b99f900767548c3bce7f8dc9c4fe8.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7264b2d5c1a89622d12be944bae7b3ee.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设曲线
![](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/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c38f266df4834d1e546d66547b80220.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb12c461e3a6e44876722986d17e3acb.png)
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名校
2 . 在直角坐标系
中,直线
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,曲线
的极坐标方程为
.
(1)求直线
的普通方程和曲线
的直角坐标方程;
(2)若点
是直线
上的一点,过点
作曲线
的切线,切点为
,求
的最小值.
![](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/421c1dff952a7bbc31f60bbdf02b13b1.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e9ba59f99418c3a3b73e36b36434b38.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/084cf5ffced059f5653ee2a1023518b7.png)
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3 . 在平面直角坐标系
中,曲线
的参数方程为
(
为参数),在以
为极点,
轴的非负半轴为极轴的极坐标系中,直线
的极坐标方程为
.
(1)求曲线
的极坐标方程;
(2)设直线
与曲线
相交于
,
两点,求
.
![](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/2043d19fa39e2562f3ceac03c27b3b21.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/35c7afba7fa24b295454141892a5a986.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/3f4dfec890cdfdda355e19463f3be813.png)
您最近一年使用:0次
2020-02-15更新
|
204次组卷
|
2卷引用:重庆市育才中学2020届高三上学期入学考试(理)数学试题
名校
4 . 在直角坐标系
中,曲线
:
(
为参数),以
为极点,
轴的非负半轴为极轴建立极坐标系.
(1)求曲线
的普通方程和极坐标方程;
(2)若射线
和
分别交曲线
于异于极点
的
,
,求
面积的最大值.
![](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/cbcf6f85690daf16ec3928834bc1f3b7.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/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若射线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17f5d2e8186f0173d7862b1d39fb3dc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1f02228e69954a6d336f4f9508000d8.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/9fd2981bf2261343f905ec1b5355a3c4.png)
您最近一年使用:0次
2019-09-26更新
|
864次组卷
|
2卷引用:重庆市南开中学2020届高三上学期第一次教学质量检测考试数学(文)试题
名校
5 . 在平面直角坐标系xOy中,射线
的普通方程为
,曲线
的参数方程为
(
为参数).以O为极点,x轴的正半轴为极轴建立极坐标系,曲线
的极坐标方程为
.
(1)写出
与
的极坐标方程;
(2)设
与
的交点为P(点P不为极点),
与
的交点为Q,当
在
上变化时,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9521988f652f79d25ed51612d6876d30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de4862bb56a0db7be04a243c91d33eb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab94459e87c666facddbe1a23ae1899d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c689c988fa72b3f23b1e912cb2e4a978.png)
(1)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)设
![](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/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab94459e87c666facddbe1a23ae1899d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f00f2f6ab162f9333ec55db195d663b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e672bc67ce824fe4ca5b887d6f9c6f3.png)
您最近一年使用:0次
2019-09-19更新
|
475次组卷
|
2卷引用:重庆市第一中学2019-2020学年高三上学期摸底考试数学(理)试题
名校
6 . 在直角坐标系
中,以坐标原点
为极点,
轴正半轴为极轴建立极坐标系,直线
(其中
)与圆
交于
两点.
(1)若
,求直线
和圆
的直角坐标方程;
(2)若
,求
.
![](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/435ca9020b2db0f638b1a94003c7742e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf6d7ffe3509860487aecae24008972.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5bbb709522dba9425a6b45ee671298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44c5ac2167a5bfc8d2d7922bc3570784.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfd975787f646f2d886715b6d3d15942.png)
![](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/d86f1b44b1b61bacc9c35d7d559a8095.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
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2018-11-22更新
|
205次组卷
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4卷引用:【市级联考】】重庆市(区县)2019年普通高等学校招生全国统一考试11月调研测试卷数学(理)试题
名校
7 . 在平面直角坐标系xOy中,曲线
的参数方程为
,曲线
的参数方程为
为参数
.
求曲线
,
的普通方程;
求曲线
上一点P到曲线
距离的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afb6101e45f8d7013bc3dc4197188c0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d22d0bbfa218014c351e508adbca3ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6acfc9319b4dfcefd8f0bb0338f7cbf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2744bbe81f3f33d56bb8c2fad914a9e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987517758fad59f6f695761deb2a5ebd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4141b26d2c32655003494a91ad6331b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afb6101e45f8d7013bc3dc4197188c0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6acfc9319b4dfcefd8f0bb0338f7cbf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65863c1abad833b79c303bfca24f535c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afb6101e45f8d7013bc3dc4197188c0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6acfc9319b4dfcefd8f0bb0338f7cbf2.png)
您最近一年使用:0次
2018-06-11更新
|
3970次组卷
|
11卷引用:重庆市中山外国语学校2019届高三上学期开学考试(9月)数学(理)试题
重庆市中山外国语学校2019届高三上学期开学考试(9月)数学(理)试题【全国校级联考】重庆市中山外国语学校2019届高三上学期开学考试(9月)数学(文)试题【校级联考】辽宁省六校协作体2019届高三上学期初联考数学(文)试题宁夏回族自治区银川市兴庆区银川一中2019-2020学年高三第五次月考数学(理)试题宁夏回族自治区银川市兴庆区银川一中2019-2020学年高三第五次月考数学(文)试题吉林省通钢一中、集安一中、梅河口五中等联谊校2019-2020学年高三下学期第五次月考数学(理)试题[全国市级联考】河南省洛阳市2017-2018学年高二质量检测数学(文)江西省南昌市东湖区第十中学2019-2020学年高二上学期期中数学试题江西省南昌市东湖区第十中学2019-2020学年高二上学期期中数学(文)试题陕西省榆林市第十中学2021-2022学年高二下学期期中文科数学试题陕西省榆林市第十中学2021-2022学年高二下学期期中理科数学试题
名校
8 . 直线
的极坐标方程为
,以极点为坐标原点,极轴为x轴建立直角坐标系,曲线C的参数方程为
(
为参数).
(1)将曲线C上各点纵坐标伸长到原来的2倍,得到曲线
,写出
的极坐标方程;
(2)射线
与
交
的交点分别为
,射线
与
和
的交点分别为
,求四边形
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a159de0b2d9eb1ae0b7e664e64d3c6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45ff62c9e84ba0ce5488b457915fc8b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c150ddb9d8bf7bb8cb7a13c000362a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07c9121cede0ee0562e23b8a26b34616.png)
(1)将曲线C上各点纵坐标伸长到原来的2倍,得到曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/211b9e53e4677ae9e2b20d5f7ce0a4e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/211b9e53e4677ae9e2b20d5f7ce0a4e4.png)
(2)射线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8ffb8bbe068309c652bfa5ff59fe0d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/211b9e53e4677ae9e2b20d5f7ce0a4e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a159de0b2d9eb1ae0b7e664e64d3c6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94165c5047e68e952df7a8dc6dc32fda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1f4a7ab352f862c528330a324e40652.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/211b9e53e4677ae9e2b20d5f7ce0a4e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a159de0b2d9eb1ae0b7e664e64d3c6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16e4e4c7a79d9d3cdb9ac5949d53e33e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e53abbd672b82a02c4975f99fbbd2c37.png)
您最近一年使用:0次
2018-04-23更新
|
1230次组卷
|
6卷引用:2020届重庆外国语学校高三上期入学检测数学理科试题
9 . 选修4-4:坐标系与参数方程
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,两种坐标系中取相同的单位长度,直线
的极坐标方程
.
(Ⅰ)当
时,判断直线
与
的关系;
(Ⅱ)当
上有且只有一点到直线
的距离等于
时,求
上到直线
距离为
的点的坐标.
在平面直角坐标系中,圆
![](https://img.xkw.com/dksih/QBM/2016/10/14/1573069407420416/1573069413883904/STEM/95266b8cdc454d51a220b85799267d77.png)
![](https://img.xkw.com/dksih/QBM/2016/10/14/1573069407420416/1573069413883904/STEM/456108c63a87410aa0fa2dcebdfc107d.png)
![](https://img.xkw.com/dksih/QBM/2016/10/14/1573069407420416/1573069413883904/STEM/6c5dd7795a0c4e3baf2192ba696d5cc0.png)
![](https://img.xkw.com/dksih/QBM/2016/10/14/1573069407420416/1573069413883904/STEM/a217b7683ab541e18ca816f30d665329.png)
![](https://img.xkw.com/dksih/QBM/2016/10/14/1573069407420416/1573069413883904/STEM/fc7b22a3fc0d4152845c6edc17564b07.png)
![](https://img.xkw.com/dksih/QBM/2016/10/14/1573069407420416/1573069413883904/STEM/40e5095b2d67434e8947c442fd24bddc.png)
(Ⅰ)当
![](https://img.xkw.com/dksih/QBM/2016/10/14/1573069407420416/1573069413883904/STEM/f7e13b6798504ac8a282a1af06cab2e7.png)
![](https://img.xkw.com/dksih/QBM/2016/10/14/1573069407420416/1573069413883904/STEM/fc7b22a3fc0d4152845c6edc17564b07.png)
![](https://img.xkw.com/dksih/QBM/2016/10/14/1573069407420416/1573069413883904/STEM/95266b8cdc454d51a220b85799267d77.png)
(Ⅱ)当
![](https://img.xkw.com/dksih/QBM/2016/10/14/1573069407420416/1573069413883904/STEM/95266b8cdc454d51a220b85799267d77.png)
![](https://img.xkw.com/dksih/QBM/2016/10/14/1573069407420416/1573069413883904/STEM/fc7b22a3fc0d4152845c6edc17564b07.png)
![](https://img.xkw.com/dksih/QBM/2016/10/14/1573069407420416/1573069413883904/STEM/737c4d65085840ee968391ad2577f3da.png)
![](https://img.xkw.com/dksih/QBM/2016/10/14/1573069407420416/1573069413883904/STEM/95266b8cdc454d51a220b85799267d77.png)
![](https://img.xkw.com/dksih/QBM/2016/10/14/1573069407420416/1573069413883904/STEM/fc7b22a3fc0d4152845c6edc17564b07.png)
![](https://img.xkw.com/dksih/QBM/2016/10/14/1573069407420416/1573069413883904/STEM/30ffdba029264ceeb75887e2506d0083.png)
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2016-12-04更新
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5卷引用:2017届重庆市育才中学高三上学期入学考试数学(理)试卷