1 . 在平面直角坐标系
中,直线的参数方程为
(t为参数),以O为极点,x正半轴为极轴建立极坐标系,曲线C的极坐标方程为
.
(1)求曲线C的直角坐标方程;
(2)设直线l与曲线C交于
两点,点D是
的中点,点
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80ec4ec4b327af5ca3338b5045a707aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44b76b143472a0cecddb774aa05806d1.png)
(1)求曲线C的直角坐标方程;
(2)设直线l与曲线C交于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2ba2238d6afe0187534155dd9ac48c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e10a3ac56219d8d2c8ce674877c8f39f.png)
您最近一年使用:0次
2020-07-16更新
|
425次组卷
|
3卷引用:2020届重庆市南开中学高三高考模拟数学(理)试题
名校
2 . 如图,在极坐标系
中,
,
,弧
,
,
所在圆的圆心分别为
,
,
,曲线
是弧
,曲线
是弧
,曲线
是弧
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/13/d6fb9080-5176-4662-b0ed-88354c403b17.png?resizew=154)
(1)写出曲线
,
,
的极坐标方程;
(2)曲线
由
,
,
构成,若曲线
的极坐标方程为
(
,
,
,
),写出曲线
与曲线
的所有公共点(除极点外)的极坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3e5af20b2f8c1fba4470f9650989e51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86371399e95723ce2ff95c3f921f69fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c850811ba59a05e945a665196539a048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ca22820119e278b5a20ad43832e8b03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b16fe2089c91dad25877895cee58f0b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4664e5ca6947382f397b5c69c7c77b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7a999c36de5c9a9ce876a4a56fa34c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07c22b1e5f86598a830d503d0746f81d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b104090ea2ac34be58a76a4e0e95cb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ca22820119e278b5a20ad43832e8b03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df1d9b712b639c8b6809c9f3ae03706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b16fe2089c91dad25877895cee58f0b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32efe4eff75508cb93e828c735dcb695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/13/d6fb9080-5176-4662-b0ed-88354c403b17.png?resizew=154)
(1)写出曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b104090ea2ac34be58a76a4e0e95cb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df1d9b712b639c8b6809c9f3ae03706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32efe4eff75508cb93e828c735dcb695.png)
(2)曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b104090ea2ac34be58a76a4e0e95cb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df1d9b712b639c8b6809c9f3ae03706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32efe4eff75508cb93e828c735dcb695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72fa71450b470cb7d6464339873d74b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc0467f0dd7d53d1bc0f25747e5f9d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/278949a1dbbe742ef4dfb4596fd94911.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a882037b9ce104ecc496e0f31a139361.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72fa71450b470cb7d6464339873d74b8.png)
您最近一年使用:0次
2020-05-22更新
|
401次组卷
|
2卷引用:重庆市八中2019-2020学年高三下学期第4次月考数学(文)试题
3 . 点
的极坐标为
,圆
的极坐标方程为
.点
为圆
上一动点,线段
的中点为点
.
(1)求点
的轨迹方程
;
(2)设线段
的中点为点
,直线
过点
且与圆
交于
两点,直线
交轨迹
于
两点,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94869ae8f4e594e8a38a5549006f444d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/925b34a1e7a48f450d883f9a0197e5c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d4aca03910382accfe738520daf689c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)设线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65436512ecbaefba4ac8123c55094211.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/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19b6d2f979a5bd9f9f7fb86f46fc1cc8.png)
您最近一年使用:0次
2020-05-14更新
|
302次组卷
|
2卷引用:重庆市巴蜀中学2019-2020学年高三下学期高考适应性月考(六)数学(理)试题
名校
4 . 如图,在以
为极点,
轴为极轴的极坐标系中,圆
,
,
的方程分别为
,
,
.
![](https://img.xkw.com/dksih/QBM/2020/4/22/2446876547817472/2447572678582272/STEM/32447674420740dfa305db7f83dca292.png?resizew=185)
(1)若
相交于异于极点的点
,求点
的极坐标
;
(2)若直线
与
分别相交于异于极点的
两点,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3e5af20b2f8c1fba4470f9650989e51.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/ab94459e87c666facddbe1a23ae1899d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69cf89e94eb51129f144d9809ec290f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b02445be519388d13bb04589de4155.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eec9cb73e1c6dc918ff416c3e0fd477c.png)
![](https://img.xkw.com/dksih/QBM/2020/4/22/2446876547817472/2447572678582272/STEM/32447674420740dfa305db7f83dca292.png?resizew=185)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9feabc99f62ee569b460e61526e2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6f29b74781deb73971d5f322927095d.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e5012e29ed018d28abf295ba6c66ab5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8add39d0693fd42ebe2fbadb601c47ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaff41080fdea43eea7efedf9ebc1498.png)
您最近一年使用:0次
2020-04-23更新
|
1524次组卷
|
9卷引用:重庆市渝西中学2020届高三下学期第四次月考数学(理)试题
重庆市渝西中学2020届高三下学期第四次月考数学(理)试题贵州省普通高等学校招生2019-2020学年高三适应性测试理科数学试题贵州省普通高等学校招生2019-2020学年高三适应性测试文科数学试题贵州省2019-2020学年高三(4月份)高考模拟(文科)数学试题湖南省怀化市2020届高三下学期6月第三次模拟考试文科数学试题湖南省怀化市2020届高三下学期6月第三次模拟考试理科数学试题贵州省2019-2020学年高三(4月份)模拟数学(理科)试题福建省厦门市湖滨中学2020届高三下学期测试数学(理)试题(已下线)专题11-1 参数方程与极坐标大题15种归类-2022年高考数学毕业班二轮热点题型归纳与变式演练(全国通用)
名校
5 . 在平面直角坐标系
中,以原点
为极点,
轴正半轴为极轴建立极坐标系.已知圆
的极坐标方程为
,圆
的直角坐标方程为
.
(1)求
与
交点的极坐标;
(2)若点
分别为圆
,
上的点,且
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.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/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f917a2022014d9c19c29eeac84c74e2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/550d183b05000722c74baf25eb4a6741.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.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/1d162c29b1e484cfc87350dd68f00b85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
您最近一年使用:0次
名校
6 . 在平面直角坐标系xOy中,以坐标原点O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
.
(1)求曲线C的直角坐标方程;
(2)若直线l的参数方程为
,(t为参数,
),点
,直线l交曲线C于A,B两点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51210b3089600f82115be9b3ee79c629.png)
(1)求曲线C的直角坐标方程;
(2)若直线l的参数方程为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71ac10ec0f5c9715280c48430d9ed15c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a06beba640fa977851bbac6593de7fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f449cadb49859b80c31ef1f68bfe81b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04a3f21d4d834ba5b8b80dd56732c136.png)
您最近一年使用:0次
2020-02-07更新
|
1264次组卷
|
11卷引用:2020届重庆市高三上学期期末测试卷理科数学( 一诊康德卷)
2020届重庆市高三上学期期末测试卷理科数学( 一诊康德卷)2020届重庆市高三上学期期末测试卷文科数学( 一诊康德卷)重庆市渝高中学2019-2020学年高三下学期4月月考数学(文)试题陕西省西安市高新一中2019-2020学年高三上学期期末文科数学试题陕西省西安市高新一中2019-2020学年高三上学期期末理科数学试题(已下线)第十五单元 不等式选讲(选讲)(B卷 滚动提升检测)-2021年高考数学(理)一轮复习单元滚动双测卷(已下线)第十四单元 不等式选讲(选讲)(B卷 滚动提升检测)-2021年高考数学(文)一轮复习单元滚动双测卷陕西省宝鸡市陈仓区2021届高三下学期第一次质量检测理科数学试题陕西省宝鸡市陈仓区2021届高三下学期第一次质量检测文科数学试题四川省绵阳南山中学2021-2022学年高三上学期入学考试数学(理)试题四川省绵阳南山中学双语学校2021-2022届高三上学期入学考试数学(理)试卷
名校
7 . 在平面直角坐标系
中,以原点
为极点,
轴正半轴为极轴建立极坐标系,已知圆
的极坐标方程为
,圆
的直角坐标方程为
.
(1)求
与
在第一象限的交点的极坐标;
(2)若点
,
分别为圆
,
上位于第一条限的点,且
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.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/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/094ab3a9f3a40f6fc88a4184371dc745.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e383fcc122f267043fbafe0972bfb900.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)若点
![](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/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d162c29b1e484cfc87350dd68f00b85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
您最近一年使用:0次
2020-01-06更新
|
626次组卷
|
5卷引用:重庆市南开中学2019-2020学年高三第五次教学质量检测考试理科数学
名校
8 . 在平面直角坐标系
中,曲线
.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
的极坐标方程和直线
的普通方程;
(2)直线
与直线
交于点
,与曲线
交于
两点,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3710e53a7436144e41fbbd0bf74d958e.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/4af15d903969c5ddfadf1a1208ad42c9.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f79bcc411adf626042e23cb46509626d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/027508515ba522b60d946110748e987b.png)
您最近一年使用:0次
2020-02-24更新
|
682次组卷
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4卷引用:重庆市第一中学2019届高三下学期4月月考(理)数学试题
9 . 在直角坐标系xOy中,直线l的参数方程为
(t为参数,
),若以原点为极点,x轴正半轴为极轴建立极坐标系,曲线E的极坐标方程为
,直线l与曲线E交于A,B两点.
(1)若
求
;
(2)当
变化时,求弦AB中点M的轨迹方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/954f6d453a9bf808214dffd9d904e7f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f63dc02238b087ff47e9aa5bf6759d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d44ff73d1c293d3461442dd1b5359d9.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfc316f251b316a8a62c60017289cc80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
您最近一年使用:0次
名校
10 . 如图所示,“8”是在极坐标系Ox中分别以
和
为圆心,外切于点O的两个圆.过O作两条夹角为
的射线分别交⊙C1于O、A两点,交⊙C2于O、B两点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/3bbce2f5-f194-4814-91a4-c26443bac12a.png?resizew=125)
(1)写出⊙C1与⊙C2的极坐标方程;
(2)求△OAB面积最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6d86c050dd27bdd08af918b0869577d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b76070841934b4480f9652a95e43cc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65af1d6b6b831ebbdc36dda5f304a3a1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/3bbce2f5-f194-4814-91a4-c26443bac12a.png?resizew=125)
(1)写出⊙C1与⊙C2的极坐标方程;
(2)求△OAB面积最大值.
您最近一年使用:0次
2019-12-23更新
|
1092次组卷
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9卷引用:重庆市南开中学2019-2020学年高三下学期第六次教学质量检测数学(文)试题
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