1 . 已知极坐标系的极点为平面直角坐标系
的原点,极轴为x轴的正半轴,曲线C的参数方程为
(
为参数),直线l的极坐标方程为
,射线
的极坐标方程为
.
(1)求曲线C的极坐标方程;
(2)已知射线
与曲线C的交点为O,P,与直线l的交点为Q,求线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d3996a4299a7d762595a572f77f9eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b88f99c06677d14d1a4879fc6842776.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed878ef20dd55a8d7ad6861d44bec611.png)
(1)求曲线C的极坐标方程;
(2)已知射线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
您最近一年使用:0次
2 . 在直角坐标系xOy中,曲线
的直角坐标方程为
.以坐标原点为极点,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)求曲线
的参数方程和
的直角坐标方程;
(2)射线
与曲线
,
分别交于
两点,求线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f44879caa04f7fad9817ae065606479d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1eaf8ac09a31e869c3310c0c381c1fb.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)射线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/388b1436ba147782851d2d290f9a0f95.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/6f44755c5fee4b90266eac73ad47a128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
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2022-05-04更新
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315次组卷
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2卷引用:陕西省西安市阎良区关山中学2021-2022学年高二下学期期中文科数学试题
3 . 在直角坐标系
中,曲线
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,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)过原点且倾斜角为锐角的直线与曲线
,直线
分别交于
两点,且
,求该倾斜角的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7795aec93c2c7ac2fd93e6747ca6516c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd383b772a2b72a1ca12148eaa852f6b.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/757cc2f991fc97a773ceffbbd3a041fa.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)过原点且倾斜角为锐角的直线与曲线
![](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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c625d16a884aa69c757f2aece677ae50.png)
您最近一年使用:0次
名校
4 . 在平面直角坐标系xOy中,曲线C的参数方程为
,
,点
,以坐标原点O为极点,x轴为正半轴为极轴的建立极坐标系.
(1)求曲线C的极坐标方程;
(2)过坐标原点O任作直线l与曲线C交于E、F两点,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5461e6bfa77dbdb8ea0add650dbeb8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f687593cb4ecef31667bf2320fdfe000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a18a7caa080988802ba1145b4fe4203.png)
(1)求曲线C的极坐标方程;
(2)过坐标原点O任作直线l与曲线C交于E、F两点,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3cfcc8a1cc42fdadd5053172bb7d0c9.png)
您最近一年使用:0次
2022-04-26更新
|
1208次组卷
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7卷引用:江西省景德镇市2022届高三第三次质检数学(文)试题
名校
5 . 在直角坐标系xOy中,
的圆心
,半径为2,以O为极点,x轴非负半轴为极轴建立极坐标系,直线
的极坐标方程是
.
(1)求
的极坐标方程和直线
的直角坐标方程;
(2)若直线
与
相交于A、B两点,求线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/669e8dfb2b45e6f74d86408343a18fe2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4f8edea2e5d4e08cf6210d0e9f3fdbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35c7afba7fa24b295454141892a5a986.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/669e8dfb2b45e6f74d86408343a18fe2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/669e8dfb2b45e6f74d86408343a18fe2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2022-04-26更新
|
816次组卷
|
4卷引用:陕西省咸阳市2022届高三下学期三模文科数学试题
名校
6 . 在直角坐标系
中,曲线
的参数方程为
(
为参数),以直角坐标原点
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)若
、
是曲线
上的两点,且
,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/aed1e7752efa29d6a3003e638da57025.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)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1695034a4c212e5568fe41625fd2a417.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf2743c965e63b856f45c9e581fcf719.png)
您最近一年使用:0次
2022-04-25更新
|
703次组卷
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4卷引用:江西省萍乡市2022届高三高考二模数学(文)试题
江西省萍乡市2022届高三高考二模数学(文)试题江西省萍乡市2022届高三高考二模数学(理)试题(已下线)押全国卷(理科)第22题 坐标系与参数方程-备战2022年高考数学(理)临考题号押题(全国卷)陕西省西安交通大学附属中学2022届高三下学期第七次模拟考试理科数学试题
7 . 在平面直角坐标系
中,已知曲线
与曲线
(
为参数),以坐标原点O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)在极坐标系中,已知射线
:
(
),
,若
与
、
的公共点分别为
、
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7795aec93c2c7ac2fd93e6747ca6516c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a55e67ae5ccd06b409b0aefc03be8e7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1cdc07f4e0e90b04d69f15613c0d81e.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/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)在极坐标系中,已知射线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17f5d2e8186f0173d7862b1d39fb3dc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7026315511e1afd55a97b5278b0dd2cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/497e43425056efa33f94f2d30a9b1d29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/71d76e2fd46060bc0124d911379473f0.png)
您最近一年使用:0次
2022-04-24更新
|
1196次组卷
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4卷引用:河南省五市2022届高三第二次联合调研考试数学(理科)试题
8 . 在直角坐标系xOy中,曲线C的参数方程是
(
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的极坐标方程;
(2)射线
(
且
)与曲线C分别交于点A,B,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43df4ef305400ba85a146923f9f212e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
(1)求曲线C的极坐标方程;
(2)射线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17f5d2e8186f0173d7862b1d39fb3dc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c04ca22dba343e23584976deeedf071f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f7fdccadfa7469825f8a5ccbf495c24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37b337c93f29459c8f59a0e1cf2d94e3.png)
您最近一年使用:0次
2022-04-24更新
|
841次组卷
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5卷引用:山西省2022届高三第二次模拟数学(文)试题
名校
解题方法
9 . 在平面直角坐标系xOy中,曲线
的参数方程为
(
为参数),曲线
的参数方程为
(
为参数)射线
:
与曲线
交于点A,射线
:
与曲线
交于点B.以原点O为极点,x轴的正半轴为极轴建立极坐标系;
(1)直接写出曲线
、射线
的极坐标方程.
(2)求△AOB的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be56fe0ce4d41bdc98ac1d9f0568d209.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/3463a6a86982aa896c2f394e98bab48e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f30698ae18bb493417f13a78a5432844.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f2d76ca62763b23a057de713440d1da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(1)直接写出曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
(2)求△AOB的面积.
您最近一年使用:0次
2022-04-22更新
|
666次组卷
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5卷引用:云南省2022届高三第二次高中毕业生复习统一检测数学(理)试题
名校
10 . 如图,在平面直角坐标系
中,以坐标原点为极点,极轴所在的直线为
轴,建立极坐标系,曲线
是经过极点且圆心在极轴上直径为2的圆,曲线
是著名的笛卡尔心形曲线,它的极坐标方程为
.
![](https://img.xkw.com/dksih/QBM/2022/4/20/2962120164728832/2963635914989568/STEM/700717a8-560b-49eb-bcd5-62f4eb783ab2.png?resizew=284)
(1)求曲线
的极坐标方程,并求曲线
和曲线
交点(异于极点)的极径;
(2)曲线
的参数方程为
(
为参数).若曲线
和曲线
相交于除极点以外的
,
两点,求线段
的长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.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/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92ca99980e4abc7c8e7b5e54c1dda97c.png)
![](https://img.xkw.com/dksih/QBM/2022/4/20/2962120164728832/2963635914989568/STEM/700717a8-560b-49eb-bcd5-62f4eb783ab2.png?resizew=284)
(1)求曲线
![](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/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab94459e87c666facddbe1a23ae1899d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f576b1012114c69877966d822064db9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab94459e87c666facddbe1a23ae1899d.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/411461db15ee8086332c531e086c40c7.png)
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2022-04-22更新
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1347次组卷
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11卷引用:内蒙古自治区赤峰市2022届高三模拟考试数学(文科)4月20日试题
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