1 .
在平面直角坐标系
中,以
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
,直线
的方程为
(
为参数).
(Ⅰ)求曲线
的直角坐标方程及直线
的普通方程;
(Ⅱ)若曲线
的参数方程为
(
为参数),曲线
上点
的极坐标为
,
为曲线
上的动点,求
的中点
到直线
距离的最大值.
在平面直角坐标系
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f2beb91f10d2d8f2aa0dcc3f5cd1598.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/afb6101e45f8d7013bc3dc4197188c0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad50dd434a36f691c6f3ccaf7b394e19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14df43239cc2b7786ea8bccecb12b7a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(Ⅰ)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afb6101e45f8d7013bc3dc4197188c0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(Ⅱ)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6acfc9319b4dfcefd8f0bb0338f7cbf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/762b8d8ae09935f8f4593889bf4e1731.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afb6101e45f8d7013bc3dc4197188c0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be7666aa2f82cd9e8bfaf54191d140eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6acfc9319b4dfcefd8f0bb0338f7cbf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e430f13f42cf2d44aa0f0e20b959684f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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2017-05-19更新
|
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6卷引用:2017届辽宁省大连市高三第一次模拟考试数学理试卷
名校
2 . 在极坐标系下,点
是曲线
上的动点,
,线段
的中点为
,以极点为原点,极轴为
轴正半轴建立平面直角坐标系.
(1)求点
的轨迹
的直角坐标方程;
(2)若轨迹
上点
处的切线斜率的取值范围是
,求点
横坐标的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16560f3cdfc0b4d64a4747d89db29bbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60d295a4cc3a58f9f38ee98337313c81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若轨迹
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f20e609302d55e497c6c543883899be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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2017-03-12更新
|
3169次组卷
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3 . 坐标系与参数方程
在极坐标系中,已知圆
的方程是
,直线
的方程是
.
(1)以极点
为原点,极轴为
轴正半轴,建立平面直角坐标系,将直线
与圆
的极坐标方程化为直角坐标方程;
(2)求直线
与圆
相交所得的弦长.
在极坐标系中,已知圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68fefd9ea573e8cede2822a518fc639e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff6e53ff96d0ef95a7bc498b11b23f7a.png)
(1)以极点
![](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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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2012·辽宁大连·二模
4 . 选修4-4:坐标系与参数方程
已知极坐标的极点在平面直角坐标系的原点
处,极轴与
轴的正半轴重合,且长度单位相同.直线
的极坐标方程为:
,点
,参数
.
(Ⅰ)求点
轨迹的直角坐标方程;
(Ⅱ)求点
到直线
距离的最大值.
已知极坐标的极点在平面直角坐标系的原点
![](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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://img.xkw.com/dksih/QBM/2013/2/22/1571118785626112/1571118791401472/STEM/6fd1130fe3e84a8da2befe6684539108.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1d123545042e2749d658947028a4e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9f332ecb7ce1805bb38c5d389a372b1.png)
(Ⅰ)求点
![](https://img.xkw.com/dksih/QBM/2013/2/22/1571118785626112/1571118791401472/STEM/d0c3452308a04757914227f3fba37534.png)
(Ⅱ)求点
![](https://img.xkw.com/dksih/QBM/2013/2/22/1571118785626112/1571118791401472/STEM/d0c3452308a04757914227f3fba37534.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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5 . 选修4-4:坐标系与参数方程
直角坐标系中,以原点为极点,
轴的正半轴为极轴建立极坐标系,圆
的极坐标方程为
,直线
的参数方程为:
(
为参数).
(Ⅰ)写出圆
和直线
的普通方程;
(Ⅱ)点
为圆
上动点,求点
到直线
的距离的最小值.
直角坐标系中,以原点为极点,
![](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/01d321b3d49bac3734fa5c6bcedb7fa0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bb54590ba7e60e39959c8df064a9213.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(Ⅰ)写出圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(Ⅱ)点
![](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)
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2016-12-04更新
|
384次组卷
|
3卷引用:【全国市级联考】辽宁省大连市2017-2018学年高二下学期期末考试数学(理)试题
6 . 选修4-4:坐标系与参数方程
已知圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5bbb709522dba9425a6b45ee671298.png)
(
为参数)和直线
,(其中
为参数,
为直线
的倾斜角).
(Ⅰ)求圆C的极坐标方程;
(Ⅱ)如果直线
与圆
有公共点,求
的取值范围.
已知圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5bbb709522dba9425a6b45ee671298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27f22f76ff1ae2c3632a00aa6471969b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dfc0a3b1258ac8a3fe7315f1af54845.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(Ⅰ)求圆C的极坐标方程;
(Ⅱ)如果直线
![](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/e170f206fdbbd834aad7580c727e2cc6.png)
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名校
7 . 选修4-4:坐标系与参数方程
在以直角坐标原点
为极点,
的非负半轴为极轴的极坐标系下,曲线
的方程是
,将
向上平移1个单位得到曲线
.
(Ⅰ)求曲线
的极坐标方程;
(Ⅱ)若曲线
的切线交曲线
于不同两点
,切点为
.求
的取值范围.
在以直角坐标原点
![](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/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80dd5d8c820a9001b3b8e870a5baade8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(Ⅰ)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.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/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/595d2bd84108a66acd10fa416f37b26d.png)
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2016-12-04更新
|
647次组卷
|
9卷引用:2015-2016学年辽宁瓦房店市高级中学高二下期末数学(理)试卷
8 . 在直角坐标平面内,直线l过点P(1,1),且倾斜角α=
.以坐标原点O为极点,x轴的非负半轴为极轴建立极坐标系,已知圆C的极坐标方程为ρ=4sin θ.
(1)求圆C的直角坐标方程;
(2)设直线l与圆C交于A,B两点,求|PA|·|PB|的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af9955b5aebb73cd84447e8541f901ac.png)
(1)求圆C的直角坐标方程;
(2)设直线l与圆C交于A,B两点,求|PA|·|PB|的值.
您最近一年使用:0次
2016-12-03更新
|
1213次组卷
|
7卷引用:2016届辽宁省大连市八中高三12月月考文科数学试卷
2016届辽宁省大连市八中高三12月月考文科数学试卷2016届福建省四地六校高三上学期10月联考理科数学试卷(已下线)二轮复习 【理】专题20 坐标系与参数方程 押题专练(已下线)二轮复习【文】专题18 坐标系与参数方程 押题专练吉林省四平市公主岭市2018-2019学年高二下学期期末数学(文)试题吉林省四平市公主岭市2018-2019学年高二下学期期末数学(理)试题(已下线)专题13.3 选修4-4 坐标系与参数方程单元检测-2021届高考数学(理)一轮复习讲练测
名校
9 . 在平面直角坐标系中,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
,过点
的直线
的参数方程为
(
为参数),直线
与曲线
交于
两点.
(1)写出曲线
的直角坐标方程和直线
的普通方程;![](https://img.xkw.com/dksih/QBM/2019/5/7/2198421159116800/2198711721345024/STEM/47e43cb648924ef0be302c7a1c22b50c.png?resizew=12)
(2)若
成等比数列,求
的值.
![](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/349d829ece278ac2156c2a86979098f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37265a2c5a6db6e7571f16286aaed83e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/887172fcd263002e17d7ff532db4a0f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](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)
(1)写出曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://img.xkw.com/dksih/QBM/2019/5/7/2198421159116800/2198711721345024/STEM/47e43cb648924ef0be302c7a1c22b50c.png?resizew=12)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54093ce9e1db41211adb0d37b35261bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2016-12-03更新
|
1165次组卷
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9卷引用:辽宁省庄河市高级中学、沈阳市第二十中学2018届高三上学期第一次联考数学(理)试题
辽宁省庄河市高级中学、沈阳市第二十中学2018届高三上学期第一次联考数学(理)试题2014-2015学年河南省南阳市高二下学期期末文科数学试卷12014-2015学年河南省南阳市高二下学期期末文科数学试卷22017届江西吉安一中高三上学期段考一数学(文)试卷宁夏育才中学2016-2017学年高二下学期期末考试数学(理)试题湖南师范大学附属中学2018届高三上学期月考试卷(三)(11月)数学理试题【校级联考】河南省顶级名校2019届高三质量测评数学理试题【市级联考】福建省福州市2018-2019学年高二下学期期中联考数学(理)试题(已下线)【南昌新东方】江西师大附中2020-2021学年高三上学期10月第一次月考数学(理)试题
名校
10 . 在平面直角坐标系中,以坐标原点为极点,x轴的正半轴为极轴建立极坐标系,已知曲线C的极坐标方程为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c68fe867846a0e12ddb5fda19a5f0019.png)
=
(
>0),过点
的直线
的参数方程为
(t为参数),直线
与曲线C相交于A,B两点.
(Ⅰ)写出曲线C的直角坐标方程和直线
的普通方程;
(Ⅱ)若
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c68fe867846a0e12ddb5fda19a5f0019.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc53248013ea8c1d69fc895f534a3a21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d74ee814026da8977561dfe7d911c6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8b3f2a9e7fe5e3c02c915df624a7d57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62ac404070de6687f108592ec81834f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(Ⅰ)写出曲线C的直角坐标方程和直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b74007f8834c06212e360621f23f4429.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2016-12-03更新
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13卷引用:辽宁省大连育明高级中学2018-2019学年高二下学期期末数学(文)试题
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