1 . 在直角坐标系xOy中,直线l的参数方程为
(t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,曲线C的极坐标方程为
,直线l与曲线C交于不同的两点A,B.
(1)求曲线C的参数方程;
(2)若点P为直线与x轴的交点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d584299329612c7a976150ec2d71456.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e0cb878349009a779d94b1bc40319bb.png)
(1)求曲线C的参数方程;
(2)若点P为直线与x轴的交点,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95188877ae2e12a26c680d1eb4d42729.png)
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名校
解题方法
2 . 已知直线l的参数方程为
(t为参数),圆C的参数方程为
(
为参数).
(1)求直线l和圆C的普通方程;
(2)若直线l与圆C有公共点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/587e0c3761c27632868fc0d5385ba010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4b1b0d9218b6b4cc611b3551561bd39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(1)求直线l和圆C的普通方程;
(2)若直线l与圆C有公共点,求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2020-06-12更新
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13卷引用:【校级联考】广东省深圳市四校发展联盟体2018-2019学年高二第二学期期中考试数学文科试题
【校级联考】广东省深圳市四校发展联盟体2018-2019学年高二第二学期期中考试数学文科试题2016-2017学年内蒙古集宁一中高二上学期期末考试数学(文)试卷山东省淄博市淄川中学2018届高三上学期开学考试数学(文)试题人教A版 全能练习 选修4-4 综合测评 模块结业测评(三)陕西省延安市第一中学2019-2020学年高二下学期期中数学(文)试题云南省保山第九中学2021届高三上学期阶段测试文科数学试题山西省怀仁市大地学校2020-2021学年高二下学期第三次月考数学(理)试题山西省怀仁市大地学校2020-2021学年高二下学期第三次月考数学(文)试题陕西省咸阳市武功县普集高中2021-2022学年高三上学期第四次月考文科数学试题(已下线)第56讲 参数方程(讲) — 2022年高考数学一轮复习讲练测(课标全国版)陕西省咸阳市武功县普集高中2021-2022学年高三上学期期末文科数学试题内蒙古通辽市科尔沁左翼中旗实验高级中学2023届高三第二次模拟考试数学试题(已下线)专题26 极坐标与参数方程(文理通用)
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3 . 已知直线
的方程为
,圆
的参数方程为
(
为参数),以原点为极点,
轴正半轴为极轴,建立极坐标系.
(1)求直线
与圆
的交点的极坐标;
(2)若
为圆
上的动点,求
到直线
的距离
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fceb9eb57ca36db386ffafeda213599c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77d1317c667c357f0a574896e69b02a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/dad2a36927223bd70f426ba06aea4b45.png)
![](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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
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2016-12-13更新
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7卷引用:【全国百强校】广东省深圳外国语学校2019届高三分班考试数学(理)试卷
4 . 已知平面直角坐标系xOy中,曲线C的参数方程为
,(
为参数),以原点为极点,x轴的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的极坐标方程以及直线l的直角坐标方程;
(2)若直线
与直线l交于M,与曲线C交于O,N,若
,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e5e1a55579ca43d6fb75a93ad2237d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fa1d4eaacf033e80662f3fedd759a12.png)
(1)求曲线C的极坐标方程以及直线l的直角坐标方程;
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5442d805aaa02c31327455d702fd08ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/878a0f760f9d39c11ae061d68022efa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98013a5042685a1db94249e70c62c09a.png)
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2020-02-01更新
|
364次组卷
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2卷引用:2020届广东省深圳市高三上学期第二次教学质量检测数学(理)试题
5 . 在平面直角坐标系
中,已知曲线
:
与曲线
:
(
为参数,
).以坐标原点为极点,x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,已知点A是射线l:
(
)与
的公共点,点B是l与
的公共点,当
在区间
上变化时,求
的最大值.
![](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/5558c083d34cbb0a58d3ce1dc6f5778e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e07df38bd4e32b15a4bef7a0fddb8224.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8eccda8d08a2959b11f25c1ddf348ec.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,已知点A是射线l:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17f5d2e8186f0173d7862b1d39fb3dc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/278949a1dbbe742ef4dfb4596fd94911.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/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18c9aeed3c8c5a04e48d011c607f9142.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac0f4498f2ff1e890d75d6d51ba6cbe8.png)
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2020-03-20更新
|
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8卷引用:2019届广东省深圳中学高三5月适应性考试数学(文)试题
名校
6 . 在平面直角坐标系xOy中,直线l的参数方程为
为参数
,直线l与曲线C:
交于A,B两点
求
的长;
在以O为极点,x轴的正半轴为极轴建立极坐标系,设点P的极坐标为
,求点P到线段AB中点M的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcbcf8917f05f728aa8d33306e204b2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987517758fad59f6f695761deb2a5ebd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ab92df58ca44d596439304b5b0658f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4141b26d2c32655003494a91ad6331b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc4a5cfa2ac470df6c70c64f62deeb33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65863c1abad833b79c303bfca24f535c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/042a192b4435dc5f1d7701897e81cef2.png)
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2016-12-04更新
|
1014次组卷
|
6卷引用:广东省深圳外国语学校2019-2020学年高三下学期4月月考数学(理)试题
名校
7 . 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
的极坐标方程是
.
(1)求曲线
的直角坐标方程和直线
的普通方程;
(2)设点
,
为曲线
上的动点,求
的面积的最大值.
![](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/9b1b41582d0e975b6be1490dbe15a8d7.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/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84907e304831d421cc0f73a428ef883d.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a26e58c354e0e3043313e9dea8374a1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e42a6f817a904205aa801dbd60b99cc.png)
您最近一年使用:0次
8 . 在直角坐标系
中,直线
的参数方程为
(
为参数),直线
的参数方程为
(
为参数),设
与
的交点为
,当
变化时,
的轨迹为曲线
.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
.
(1)写出
的普通方程;
(2)求曲线
和曲线
交点的极坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f3f98eba79a32d9e88f68c771be8080.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d68a422b22ae1cb8efd718b5bcc7d17c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69cf89e94eb51129f144d9809ec290f7.png)
(1)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
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2020-02-27更新
|
284次组卷
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2卷引用:2020届广东省深圳市罗湖区高三上学期期末质量检测数学理科试题
14-15高二上·黑龙江牡丹江·期中
名校
9 . 已知直线
的参数方程:
(
为参数),曲线
的参数方程:
(
为参数),且直线交曲线
于
,
两点.
(1)将曲线
的参数方程化为普通方程,并求
时,
的长度;
(2)已知点
,求当直线倾斜角
变化时,
的范围.
![](https://img.xkw.com/dksih/QBM/2018/7/10/1985430294839296/1986211897139200/STEM/cebe3e0e4e6c43cba679cd379a11b64a.png?resizew=9)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37b6357b8d6043e32f68f4d652e58853.png)
![](https://img.xkw.com/dksih/QBM/2018/7/10/1985430294839296/1986211897139200/STEM/44fdb4c1d9e84577bd56e10f0806a03f.png?resizew=9)
![](https://img.xkw.com/dksih/QBM/2018/7/10/1985430294839296/1986211897139200/STEM/28a10f00f0a74d66a663804154770873.png?resizew=16)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dcf6b822c3fa19cd715a9783be97234.png)
![](https://img.xkw.com/dksih/QBM/2018/7/10/1985430294839296/1986211897139200/STEM/3fc694a87ea84889ba447499be2cf6f4.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2018/7/10/1985430294839296/1986211897139200/STEM/28a10f00f0a74d66a663804154770873.png?resizew=16)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)将曲线
![](https://img.xkw.com/dksih/QBM/2018/7/10/1985430294839296/1986211897139200/STEM/28a10f00f0a74d66a663804154770873.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2018/7/10/1985430294839296/1986211897139200/STEM/5162bd49efdd4255bfe1036229bc5fe7.png?resizew=43)
![](https://img.xkw.com/dksih/QBM/2018/7/10/1985430294839296/1986211897139200/STEM/070a49e5db284929bd4f6efa7645449a.png?resizew=31)
(2)已知点
![](https://img.xkw.com/dksih/QBM/2018/7/10/1985430294839296/1986211897139200/STEM/1b9b47de4fe74f1293616f0273803598.png?resizew=44)
![](https://img.xkw.com/dksih/QBM/2018/7/10/1985430294839296/1986211897139200/STEM/1fadfdbc1d934aaab1b7ec22364bae0d.png?resizew=13)
![](https://img.xkw.com/dksih/QBM/2018/7/10/1985430294839296/1986211897139200/STEM/32810b87d0b04a359966be8a6a2dbed6.png?resizew=61)
您最近一年使用:0次
2018-07-11更新
|
476次组卷
|
5卷引用:广东省深圳市耀华实验学校2017-2018学年高二下学期期末考试数学(文)试题
名校
10 . 在平面直角坐标系
中,曲线
过点
,其参数方程为
(
为参数,
),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
.
(1)写出曲线
的普通方程和曲线
的直角坐标方程;
(2)已知曲线
和曲线
交于
两点(
在
之间),且
,求实数
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/594d4b99d4c5c90fc2e8010cc198551d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/704383c9e8fc0f925b1ca70d2d6437b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.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/23dd406c6137b3ba77cc5346508eb3a4.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)已知曲线
![](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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab34ce6cee0673ab0d37b660d57bc07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2018-05-10更新
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743次组卷
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2卷引用:【全国市级联考】广东省深圳市宝安区宝安中学等2018届高三七校联合体考前冲刺交流考试数学(理)试题