1 . 在直角坐标系
中,曲线
:
经过伸缩变换
后得到曲线
,以原点
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)写出曲线
的参数方程和直线
的直角坐标方程;
(2)在曲线
上求一点
,使点
到直线
的距离最小.
![](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/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af6f8a4abae83872f6ac8eb01e6b5d7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.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/4fd348cbb513d9de58eaba0da0cee175.png)
(1)写出曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)在曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2021-04-30更新
|
1148次组卷
|
5卷引用:云南省昆明市第一中学2021届高三第八次考前适应性训练数学(文)试题
2 . 已知曲线
的极坐标方程为
,直线
的参数方程为
(
为参数)
(1)求曲线
的参数方程和直线
的普通方程;
(2)设点
是曲线
上的动点,点
,
在直线
上,且
,求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bac48ea1831290efc7269afddd3e9a29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adf9b6bb59c6f64d0a37bce262dca349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)设点
![](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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc5a5a55e915f22e5afc21330e126a03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ed4c4e8edbd179f3fc38a6653f18c1.png)
您最近一年使用:0次
2021-04-29更新
|
947次组卷
|
3卷引用:安徽省江淮十校2021届高三下学期4月第三次质量检测文科数学试题
名校
解题方法
3 . 在同一平面直角坐标系
中,经过伸缩变换
后,曲线
变为曲线
.
(1)求
的参数方程;
(2)设
,点
是
上的动点,求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/349a465a45a731182861b2ade790b16a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70feca8eac775ebee7b6d9760e2be6f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c179fe7eff7abfdd092b63c9c1b82d0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/532d9de08698f61d7c010805c61a4ec5.png)
您最近一年使用:0次
2021-04-28更新
|
544次组卷
|
2卷引用:黑龙江省大庆实验中学2020-2021学年高二下学期4月月考试卷文科数学试题
名校
解题方法
4 . 在平面直角坐标xOy中,已知曲线
的参数方程为
(
为参数),以坐标原点O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)写出曲线
的普通方程和直线l的直角坐标方程;
(2)若直线l上的两个动点M,N满足
,点P在曲线
上,以M,N,P为顶点构造平行四边形MNPQ,求平行四边形MNPQ面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4934bb9580e1b63d4eccc8189070c4e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6bdba1fe286040b38a3c4da34c95d44.png)
(1)写出曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线l上的两个动点M,N满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b23ce5966c37efe1732853c9163e915c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
您最近一年使用:0次
2021-04-27更新
|
439次组卷
|
2卷引用:河南省实验中学2020-2021学年高二下学期期中数学理科试题
5 . 知在平面直角坐标系
中,直线
的参数方程是
(
是参数),以原点
圆点;以
轴的非负半轴为极轴,且取相同的单位长度建立极坐标系,曲线
的极坐标方程为
,
(1)求直线
的普通方程与曲线
的直角坐标方程﹔
(2)
设为曲线
上任意一点,求
的取值范围.
![](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/1a0cfb02ba2ba4d48f991a33d603a3b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/152236216f8d1cb39b261108e8fc8b9e.png)
![](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/43cb11daa374ec7d2be9535c51b99c14.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d259822ab64b8626f3893b8432673358.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88584cf1df43e28d03592c7998b1653.png)
您最近一年使用:0次
2021-03-28更新
|
980次组卷
|
2卷引用:百校大联考2021届高三第六次大联考文科数学试题
名校
解题方法
6 . 已知
,则
的最大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e903ad9a2806998db8ed16283bec8568.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88584cf1df43e28d03592c7998b1653.png)
A.1 | B.![]() | C.![]() | D.6 |
您最近一年使用:0次
2021-03-28更新
|
253次组卷
|
3卷引用:黑龙江省哈尔滨市哈尔滨师范大学附属中学2020-2021学年高二上学期期末考试 数学(文)试题
7 . 在平面直角坐标系
中,
是坐标原点,以
为极点,
轴的正半轴为极轴建立极坐标系,曲线
的极坐标方程为
,曲线
的极坐标方程为
,点
是曲线
上的点,且点
的极坐标为
,
.
(1)直接写出点
的直角坐标,曲线
的直角坐标方程和曲线
的普通方程;
(2)若点
是曲线
上的点,求
的面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/9017178b7626f2bc34094ee20bcd678a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/925b34a1e7a48f450d883f9a0197e5c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b33fd52b661f25e84fa23a9719a54cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c567bb4b7f272e3fb1839d4edaea1f6f.png)
(1)直接写出点
![](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)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e112a25cc3b94c09855429e6ad3ccaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
您最近一年使用:0次
2021-03-23更新
|
290次组卷
|
2卷引用:云南省2021届高三第一次复习统一检测数学(文)试题
8 . 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,
轴的非负半轴为极轴建立极坐标系,直线
的极坐标方程为
.
(1)求曲线
的普通方程与直线
的直角坐标方程;
(2)点
为曲线
上的动点,求点
到直线
的距离的最大值.
![](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/c2f7f0a3d7f8efcef3122125312031c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.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/178d249d923f64e51ac742a37ce2f292.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2021-02-03更新
|
770次组卷
|
2卷引用:河南省信阳市2020-2021学年高二上学期期末数学(理科)试题
9 . 已知直线
的极坐标方程为
,圆
的参数方程为
(其中
为参数)
(1)判断直线
与圆
的位置关系;
(2)设点
在曲线
上,点
在直线
上,则求线段
的最小值及此时点
坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70498aca8afc1531efd39470ab91eacc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b277c8607af4373551c5e6a112d0a4cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(1)判断直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设点
![](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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d44e8bc37ed03f44470762748a8f942a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
2021-01-07更新
|
779次组卷
|
4卷引用:黑龙江省哈尔滨市第六中学2020-2021学年高二上学期期末考试数学(文)试题
名校
10 . 已知曲线
的方程为
,曲线
的参数方程为
(
为参数).
(1)求
的参数方程和
的普通方程;
(2)设点
在
上,点
在
上,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eae3f914a02c2b5b6bab4e5b1cf4f22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f3fe0dc0cfbadf6071a4ae869a5426f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)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/d44e8bc37ed03f44470762748a8f942a.png)
您最近一年使用:0次
2020-12-15更新
|
953次组卷
|
11卷引用:精做07 坐标系与参数方程、不等式选讲-备战2021年高考数学(理)大题精做
(已下线)精做07 坐标系与参数方程、不等式选讲-备战2021年高考数学(理)大题精做(已下线)解密23 坐标系与参数方程 (讲义)-【高频考点解密】2021年高考数学(理)二轮复习讲义+分层训练(已下线)解密21 坐标系与参数方程 (讲义)-【高频考点解密】2021年高考数学(文)二轮复习讲义+分层训练【市级联考】福建省漳州市2019届高三第一次教学质量检查测试文科数学试题【市级联考】福建省漳州市2019届高三第一次教学质量检查测试理科数学试题内蒙古集宁一中2018-2019学年高二下学期期末数学(文)试题2020届名校联盟高三联考评估卷(八)数学理科试题湖南省衡阳市衡阳县2018-2019学年高二下学期六科联赛数学(理)试题2020届名校联盟高三联考评估卷(八)数学文科试题(已下线)调研测试五(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新疆喀什地区普通高考2023届高三适应性检测数学(文)试题