1 . 已知曲线
的参数方程为
(
为参数),曲线
的参数方程为
(
为参数),以坐标原点O为极点,x轴的正半轴为极轴建立极坐标系,射线
的极坐标方程为
.
(1)求曲线
和曲线
的极坐标方程和射线
的平面直角坐标方程;
(2)若射线
与曲线
的交点为P,与曲线
的交点为Q,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8ebadb2acb01dc4f637ef4cc05e2e15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdf2b4b99f6e7c8d325cb0599bff506a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b3372821f274d9c2e7c9f911bd5cf26.png)
(1)求曲线
![](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/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
(2)若射线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.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/3668b55ec6c015b1afe1aabb38392a35.png)
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2022-09-23更新
|
467次组卷
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3卷引用:江西省上高二中2023届高三上学期第三次月考数学(文)试题
名校
2 . 在平面直角坐标系
中,已知直线
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
,点
的极坐标为
,且
在直线
上.
(1)求曲线
内接矩形周长的最大值.
(2)若直线
与曲线C交于
两点,求
的值;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7795aec93c2c7ac2fd93e6747ca6516c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ff49f1cffc39281fd584fdd3836f7af.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/0f7d7cef16186cba68ee038ff3927436.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba7fb9e7e0a5c8f262be498e666f6480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfdb0d7c66471e0b09ca22254aebca68.png)
您最近一年使用:0次
名校
3 . 在直角坐标系
中,直线
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
,且
与
交于
,
两点.
(1)求
的普通方程和
的直角坐标方程;
(2)设
,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/d385fea2267c6fb40eb37ed0aeadda5d.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/476df2e81365a773729d5ce002d6d5d2.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)
(1)求
![](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/a23d0aabf43bf2404ec97a0fae5c1b62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed1b3031d7393a63719166285314d73f.png)
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2022-09-08更新
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607次组卷
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5卷引用:江西省南昌市第十九中学2023届高三上学期第三次月考(10月)理科数学试题
名校
4 . 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,
轴的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
的普通方程以及直线
的直角坐标方程;
(2)点
,
分别在曲线
和直线
上,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/dbd494adc8e1ca5cc8613069218f97c5.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/6ac420a9dd99cf21278f4f9d7fa3f55f.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)点
![](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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/084cf5ffced059f5653ee2a1023518b7.png)
您最近一年使用:0次
5 . 已知点
的极坐标为
,则点
的直角坐标为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3deb2f685fff5b6053b490fab6924e21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2022-06-06更新
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9卷引用:江西省赣州市教育发展联盟2021-2022学年高二下学期第8次联考数学(文)试题
江西省赣州市教育发展联盟2021-2022学年高二下学期第8次联考数学(文)试题陕西省西安市西咸新区泾河新城第一中学2022-2023学年高二下学期5月质量检测理科数学试题陕西省安康市汉滨区七校2021-2022学年高二下学期期末联考文科数学试题新疆喀什2021-2022学年高二下学期期末考试数学(理)试题甘肃省武威市凉州区2021-2022学年高二下学期期末考试数学(文)试题新疆新和县实验中学2021-2022学年高二下学期期末考试数学(文)试题新疆新和县实验中学2021-2022学年高二下学期期末考试数学(文)试题陕西省西安市阎良区关山中学2021-2022学年高二下学期期末文科数学试题内蒙古呼伦贝尔市满洲里远方中学2021-2022学年高二下学期期末考试数学(文)试题
名校
6 . 在平面直角坐标系xOy中,曲线C的参数方程为
(
为参数),以原点O为极点,x轴的非负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)设点M的极坐标为
,直线l与曲线C交于A,B两点,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9380dca2fd7fb8d20c0f5af481d613c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/649361e842399b796c4cb0b1fe75e2d9.png)
(1)求曲线C的普通方程和直线l的直角坐标方程;
(2)设点M的极坐标为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07c22b1e5f86598a830d503d0746f81d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bba91242bb7841a41711f02db45fdc0.png)
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名校
7 . 在极坐标系
中,射线
的极坐标方程为
,曲线C的极坐标方程为
,且射线
与曲线C有异于点O的两个交点P,Q,
(1)求
的取值范围;
(2)求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3e5af20b2f8c1fba4470f9650989e51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0723ebcac812fcadbe8bec78437bcecb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a484392ff7ca307d1e8d150c4954ad0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/740717aeb9f4496d9fe30471a100008a.png)
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2022-06-05更新
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555次组卷
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3卷引用:江西省赣州市赣县第三中学2021-2022学年高二下学期6月月考数学(理)试题
江西省赣州市赣县第三中学2021-2022学年高二下学期6月月考数学(理)试题广西柳州高中、南宁二中2021-2022学年高二下学期期中联考数学(理)试题(已下线)专题12-1 参数方程与极坐标归类-1
8 . 在直角坐标系
中,曲线C的参数方程为
(
为参数),以坐标原点O为极点,x轴的非负半箱为极轴建立极坐标系,点M的极坐标为
,直线l的极坐标方程为
.
(1)求点M的直角坐标和直线l的直角坐标方程;
(2)若N为曲线C上的动点,求
的中点P到直线l的距离的最小值及此时点P的极坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5155682294d91dc2f384c2fc223e9c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92240f5cb25474f30f225f2b13d9e059.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25fb5317b989e2e4e912cd03fdba0880.png)
(1)求点M的直角坐标和直线l的直角坐标方程;
(2)若N为曲线C上的动点,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
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2022-05-19更新
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888次组卷
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3卷引用:江西省瑞金市第三中学2023届高三上学期阶段性检测(二)数学(文)试题
9 . 已知直线
的参数方程为:
(
为参数),曲线
的极坐标方程为:
.
(1)写出直线
的普通方程和曲线
的直角坐标方程;
(2)已知直线
和曲线
交于
两点,设点
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1893a54604df175280d4f705f8439673.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1846b8bc5a65506cea8e133e31618cc6.png)
(1)写出直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知直线
![](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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15ed90ebf0061c8a79beed307fc1719a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5026e1d5fcf2498b2e5ec5da4e0b11b2.png)
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2022-05-16更新
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873次组卷
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6卷引用:江西省抚州市第一中学2023届高三上学期第一次摸底考试数学(文)试题
10 . 在平面直角坐标系xOy中,直线l的参数方程为
(其中t为参数),以O为极点,x轴正半轴为极轴建立极坐标系,曲线C的极坐标方程为
.
(1)求直线l的普通方程以及曲线C的直角坐标方程;
(2)求曲线C上的点到直线l的距离的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/271e5c5d17b9998825559409bbe4695c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e7d68ecabdd18089c7ff19f19dbc83d.png)
(1)求直线l的普通方程以及曲线C的直角坐标方程;
(2)求曲线C上的点到直线l的距离的最大值.
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2022-05-15更新
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474次组卷
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3卷引用:江西省石城县赣源中学2023届高三8月月考数学(文)试题