2014高三·全国·专题练习
名校
1 . 已知曲线C的极坐标方程为ρ=4cosθ,以极点为原点,极轴为x轴正半轴建立平面直角坐标系,设直线l的参数方程为
(t为参数).
(1)求曲线C的直角坐标方程与直线l的普通方程;
(2)设曲线C与直线l相交于P,Q两点,以PQ为一条边作曲线C的内接矩形,求该矩形的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab54bdb64be2c49e03930555dd42ccb0.png)
(1)求曲线C的直角坐标方程与直线l的普通方程;
(2)设曲线C与直线l相交于P,Q两点,以PQ为一条边作曲线C的内接矩形,求该矩形的面积.
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2020-02-25更新
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371次组卷
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17卷引用:2016届海南省文昌中学高三上学期期末考试文科数学试卷
2016届海南省文昌中学高三上学期期末考试文科数学试卷(已下线)2014年高考数学文二轮专题复习与测试选修4-4坐标系与参数方程练习卷(已下线)2015届云南省玉溪一中高三上学期第一次月考理科数学试卷(已下线)2015届黑龙江省哈尔滨市六中高三上学期期中考试理科数学试卷2015届吉林省吉林市一中高三3月教学质量检测一文科数学试卷2015届甘肃省天水市一中高三5月中旬仿真考试理科数学试卷2015届甘肃省天水市一中高三5月中旬仿真考试文科数学试卷2017届江西省新余一中、宜春一中高三7月联考文科数学试卷2016届河北省邯郸市高三下第二次模拟考试数学(理)卷2016届河北省邯郸市高三下第二次模拟考试数学(文)卷广西南宁市2017届高三第一次适应性测试数学(理)试题2017届广西钦州市高三下学期普通高中毕业班第一次适应性测试(二模)数学(文)试卷2017届广西南宁市高三第一次适应性测试数学(文)试卷专题11.6 参数方程与极坐标(练)-江苏版《2020年高考一轮复习讲练测》山西省太原市实验中学校2019-2020学年高二下学期期中数学(文)试题2020届河北省衡水市枣强中学高三下学期3月模拟2数学(理)试题河北省石家庄市第二中学2020届高三下学期3月内部考试数学(理)试题
2 . 选修4—4:坐标系与参数方程
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,
轴正半轴为极轴,建立极坐标系,曲线
的极坐标方程为
.
(Ⅰ) 写出
的普通方程和
的直角坐标方程;
(Ⅱ) 设点
在
上,点
在
上,判断
与
的位置关系并求
的最小值.
在直角坐标系
![](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/1a2f43d763ff73c64a143e48e81671bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.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/9e0cb878349009a779d94b1bc40319bb.png)
(Ⅰ) 写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(Ⅱ) 设点
![](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/acc290b44635265137fdf13146b6a6d9.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/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f82358b724051b032c7ec734a226ae84.png)
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2018-08-10更新
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780次组卷
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3卷引用:【全国市级联考】海南省琼海市2018届高考模拟考试文数试卷
3 . 已知直角坐标系xOy中,直线l的参数方程为
(t为参数),以直角坐标系xOy中的原点O为极点,x轴的非负半轴为极轴,圆C的极坐标方程为ρ2-4ρcosθ+3=0.
(1)求
的普通方程及C的直角坐标方程;
(2)P为圆C上的点,求P到
的距离的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0bc30b8700c092a40086b0f200c65aa.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)P为圆C上的点,求P到
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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4 . (选修4-4:极坐标与参数方程)
在平面直角坐标系中,曲线
的参数方程
,在以O为极点,
轴的正半轴为极轴的坐标系中,曲线
是圆心在极轴上,且经过极点的圆,已知
上的点
对应的参数
,射线![](https://img.xkw.com/dksih/QBM/2016/3/18/1572545467555840/1572545473937408/STEM/e29dda93ce054a4aba66bba791cec830.png)
与曲线
交于点![](https://img.xkw.com/dksih/QBM/2016/3/18/1572545467555840/1572545473937408/STEM/b9136ec26ac14a588c55482ff3cf555b.png)
(1)求曲线
,
的直角坐标方程;
(2)若点
,
,在曲线
上,求
的值.
在平面直角坐标系中,曲线
![](https://img.xkw.com/dksih/QBM/2016/3/18/1572545467555840/1572545473937408/STEM/bde9e7223c644e7f892718a22a8e20be.png)
![](https://img.xkw.com/dksih/QBM/2016/3/18/1572545467555840/1572545473937408/STEM/bc711c6138bc4760b74b435d77b9ea23.png)
![](https://img.xkw.com/dksih/QBM/2016/3/18/1572545467555840/1572545473937408/STEM/158d2d6f7a1e4d05b869fb24cf9cd08f.png)
![](https://img.xkw.com/dksih/QBM/2016/3/18/1572545467555840/1572545473937408/STEM/cb583c3c8cb64038abf8286d33cd67b9.png)
![](https://img.xkw.com/dksih/QBM/2016/3/18/1572545467555840/1572545473937408/STEM/bde9e7223c644e7f892718a22a8e20be.png)
![](https://img.xkw.com/dksih/QBM/2016/3/18/1572545467555840/1572545473937408/STEM/9d4cb9a272e74677b05d8f662e854efa.png)
![](https://img.xkw.com/dksih/QBM/2016/3/18/1572545467555840/1572545473937408/STEM/3a1fe7439ea34387a45e6579503eb689.png)
![](https://img.xkw.com/dksih/QBM/2016/3/18/1572545467555840/1572545473937408/STEM/e29dda93ce054a4aba66bba791cec830.png)
![](https://img.xkw.com/dksih/QBM/2016/3/18/1572545467555840/1572545473937408/STEM/032ab819f99241a9b0d417e2ad753e2e.png)
![](https://img.xkw.com/dksih/QBM/2016/3/18/1572545467555840/1572545473937408/STEM/cb583c3c8cb64038abf8286d33cd67b9.png)
![](https://img.xkw.com/dksih/QBM/2016/3/18/1572545467555840/1572545473937408/STEM/b9136ec26ac14a588c55482ff3cf555b.png)
(1)求曲线
![](https://img.xkw.com/dksih/QBM/2016/3/18/1572545467555840/1572545473937408/STEM/bde9e7223c644e7f892718a22a8e20be.png)
![](https://img.xkw.com/dksih/QBM/2016/3/18/1572545467555840/1572545473937408/STEM/cb583c3c8cb64038abf8286d33cd67b9.png)
(2)若点
![](https://img.xkw.com/dksih/QBM/2016/3/18/1572545467555840/1572545473937408/STEM/bb4c93a70a244b3eab4ae780148ecb93.png)
![](https://img.xkw.com/dksih/QBM/2016/3/18/1572545467555840/1572545473937408/STEM/eb98bf39f91d4938b4f0301518c895e4.png)
![](https://img.xkw.com/dksih/QBM/2016/3/18/1572545467555840/1572545473937408/STEM/bde9e7223c644e7f892718a22a8e20be.png)
![](https://img.xkw.com/dksih/QBM/2016/3/18/1572545467555840/1572545473937408/STEM/e08262cc47b14dd3b6e202486d66c2c1.png)
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名校
5 . 在平面直角坐标系
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,得曲线
的极坐标方程为
.
(1)化曲线
的参数方程为普通方程,化曲线
的极坐标方程为直角坐标方程;
(2)直线
(
为参数)过曲线
与
轴负半轴的交点,求与直线
平行且与曲线
相切的直线方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f2beb91f10d2d8f2aa0dcc3f5cd1598.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afb6101e45f8d7013bc3dc4197188c0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d459c40729c2d23f884c19951043831c.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6acfc9319b4dfcefd8f0bb0338f7cbf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2261da04be8b203d94e310a543f93495.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/024b430708f0459c60d3bfc533f9edc0.png)
(1)化曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afb6101e45f8d7013bc3dc4197188c0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6acfc9319b4dfcefd8f0bb0338f7cbf2.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b136ae2c19988eb7c4671a6a3e89ade.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afb6101e45f8d7013bc3dc4197188c0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6acfc9319b4dfcefd8f0bb0338f7cbf2.png)
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2016-12-02更新
|
1411次组卷
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3卷引用:2015-2016学年海南文昌中学高二下期末文科数学试卷
2012·海南省直辖县级单位·一模
6 . 在直角坐标系
中,圆C的参数方程为
(
为参数
)
以O为极点,
轴的非负半轴为极轴,并取相同的长度单位建立极坐标系,直线
的极坐标方程![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5139e78ba3cec0942366acd0d7b8db4b.png)
(1)求圆心的极坐标.
(2)若圆C上点到直线
的最大距离为3,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c7929dca87e794f99640841990fd426.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45ba6b6aa6c3f9faba6b03bc193a6e61.png)
以O为极点,
![](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/5139e78ba3cec0942366acd0d7b8db4b.png)
(1)求圆心的极坐标.
(2)若圆C上点到直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
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