1 . 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,曲线
的极坐标方程为
.
(1)求曲线
的普通方程和曲线
的直角坐标方程;
(2)点
,
分别为曲线
,
上的动点,求证:
.
![](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/c7628a182e9dd68153a521c5397af24b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.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/925b34a1e7a48f450d883f9a0197e5c9.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.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/2e1da98c95d573256f89e72ca47392e0.png)
您最近一年使用:0次
2020-08-16更新
|
80次组卷
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10卷引用:广东省茂名市五校联盟2020届高三下学期第二次联考数学(理)试题
广东省茂名市五校联盟2020届高三下学期第二次联考数学(理)试题广东省茂名市五校联盟2020届高三下学期第二次联考数学(文)试题湖南省永州市六县2020届高三下学期6月第二次联考数学(文)试题湖南省永州市六县2020届高三下学期6月第二次联考数学(理)试题河北省衡水市2020届高三下学期六月联考数学(文)试题湖南省永州市宁远、道县、东安、江华、蓝山、新田2020届高三下学期六月联考文科数学试题(已下线)专题22 坐标系与参数方程-2020年高考数学(理)母题题源解密(全国Ⅱ专版)(已下线)专题22 坐标系与参数方程-2020年高考数学(文)母题题源解密(全国Ⅱ专版)湖南省永州市宁远、道县、东安、江华、蓝山、新田2020届高三下学期六月联考理科数学试题宁夏吴忠市青铜峡第一中学2020-2021年高二下学期第二次月考数学(理)试题
2 . 在极坐标系
中,曲线
的极坐标方程为
,直线
的极坐标方程为
,设
与
交于
两点,
中点为
,
的垂直平分线交
于
.以
为坐标原点,极轴为
轴的正半轴建立直角坐标系
.
(1)求
的直角坐标方程与点
的直角坐标;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3e5af20b2f8c1fba4470f9650989e51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42137d6ea5076b1385940d3450b8d087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72339e813823a31e3436cf7290af5881.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.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/7ee31829d0d4d5f779a957d7df8058ab.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87482d4cc8571f6836c3638d6aeb9fed.png)
您最近一年使用:0次
2020-08-16更新
|
420次组卷
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15卷引用:广东省广州市天河外国语学校2019-2020学年高三下学期线上测试数学(理)试题
广东省广州市天河外国语学校2019-2020学年高三下学期线上测试数学(理)试题2020届四川省宜宾市高三第二次诊断测试理科数学试题2020届四川省宜宾市高三第二次诊断检测数学(文科)试题四川省宜宾市叙州区第一中学校2019-2020学年高二下学期第四学月考试数学(理)试题四川省宜宾市叙州区第一中学校2019-2020学年高二下学期第四学月考试数学(文)试题河南省大联考2020届高三阶段性测试(七)理科数学试题河南省6.18大联考2019-2020学年高中毕业班阶段性测试(七)文科数学试题2020届河北省保定市易县中学高三模拟数学(文)试题2020届河北省保定市易县中学高三模拟数学(理)试题(已下线)专题22 坐标系与参数方程-2020年高考数学(理)母题题源解密(全国Ⅱ专版)(已下线)专题22 坐标系与参数方程-2020年高考数学(文)母题题源解密(全国Ⅱ专版)安徽省怀远一中、蒙城一中、淮南一中、颍上一中、涡阳一中2020届高三5月五校联考数学理科试题(已下线)专题22 坐标系与参数方程-2020年高考数学(文)母题题源解密(全国Ⅰ专版)(已下线)专题22 坐标系与参数方程-2020年高考数学(理)母题题源解密(全国Ⅰ专版)贵州省思南中学2023届高三数学模拟试题
3 . 在平面直角坐标系xOy中,曲线C:
经过伸缩变换
后所得曲线记为
.以O为极点,x轴的正半轴为极轴,建立极坐标系Ox.
(Ⅰ)求曲线
的极坐标方程;
(Ⅱ)已知A,B是曲线
上任意两点,且
,求证:O到直线AB的距离为常数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f5d967ad135991b6075ee45df55643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d61dedf0459a7719067c8d4d148dad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c8a9c4957431681ddfc77895a88508.png)
(Ⅰ)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c8a9c4957431681ddfc77895a88508.png)
(Ⅱ)已知A,B是曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c8a9c4957431681ddfc77895a88508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
您最近一年使用:0次
4 . 在直角坐标系
中,直线
的参数方程为
(
为参数),以O为极点,
轴的正半轴为极轴的极坐标系中,曲线
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c343c8fb0ffd723d7f35200adf71159.png)
(1)写出曲线
的直角坐标方程;
(2)设点
,
与
相交于A,B两点,与
相交于C,D两点,证明:
![](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/91c739b935d4b9e06c8ddf7670efeec2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95349927ea0096092d1f4733b55abe5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c343c8fb0ffd723d7f35200adf71159.png)
(1)写出曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9feabc99f62ee569b460e61526e2e.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6b0fc22034c9db29b23c4cf9faf5af6.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/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01eeff6623967669c2d97fed6c035e11.png)
您最近一年使用:0次
2019-12-26更新
|
299次组卷
|
2卷引用:2020 届广东省湛江市高三下学期网络教学训练题(二)文科数学试题
名校
5 . 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,曲线
的极坐标方程为
,若极坐标系内异于
的三点
,
,
都在曲线
上.
(1)求证:
;
(2)若过
,
两点直线的参数方程为
(
为参数),求四边形
的面积.
![](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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e0cb878349009a779d94b1bc40319bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81e5094ea2e1ae387f33e0b554c60b14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a4aecf3b1ceaa9b4f660030672baddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a806e583790b07ed766d51249fa013ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a653c31f6db4cfd6b6b2d7bc5a0424b.png)
(2)若过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ea6230afeaa1027dc69969cb5d74c3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5241e0e07a9cd48e4f853405dca1a03.png)
您最近一年使用:0次
2019-04-08更新
|
2892次组卷
|
14卷引用:广东省惠州市2019-2020学年高三第三次调研考试文科数学试题
广东省惠州市2019-2020学年高三第三次调研考试文科数学试题广东省惠州市2019-2020学年高三第三次调研考试理科数学试题【校级联考】江西省吉安一中、九江一中、新余一中等八所重点中学2019届高三4月联考数学(理)试题【校级联考】江西省吉安一中、九江一中、新余一中等八所重点中学2019届高三4月联考数学(文)试题【全国百强校】福建省厦门第一中学2019届高三5月市二检模拟考试数学(理)试题江西省临川二中、临川二中实验学校2019-2020学年高三上学期第三次月考数学(文)试题(已下线)2020届高三12月第01期(考点13)(文科)-《新题速递·数学》2020届高三1月(考点13-14)(理科)-《新题速递·数学》.广西名校2021届高三大联考(三)数学(文)试题广西桂林、崇左市2021届高三二模数学(理)试题陕西省西安交通大学附属中学2021届高三下学期第四次模拟考试理科数学试题广西桂林、崇左市2021届二模数学(文)试题广西名校2023届高三下学期3月份联考数学(理)试题广西名校2023届高三下学期3月份联考数学(文)试题
名校
6 . 在直角坐标系
中,椭圆
的方程为
(
为参数);以原点
为极点,以
轴正半轴为极轴建立极坐标系,圆
的极坐标方程为
.
(1)求椭圆
的极坐标方程,及圆
的直角坐标方程;
(2)若动点
在椭圆
上,动点
在圆
上,求
的最大值;
(3)若射线
分别与椭圆
交于点
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f2beb91f10d2d8f2aa0dcc3f5cd1598.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c19f6aa27953793b84fa11b586c0f281.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4644e07aac5f825bda46b9d4da62beb8.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)若动点
![](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/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86971cee973445cfa3e853edf7ffba10.png)
(3)若射线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/121eb5a2a2ad262d87967eddfe267445.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/848f0a6a566d677429c364c2da9f6404.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae50d614a8afd23b30069c46f78787a3.png)
您最近一年使用:0次
7 . 在平面直角坐标系
中,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,直线l的极坐标方程为
,曲线C的参数方程为
(
为参数,
).
(1)求直线l的直角坐标方程及曲线C的普通方程;
(2)证明:直线l和曲线C相交,并求相交弦的长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fbfa74da8baf7a1a32f4d1fbb89cef0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e006a66b83f3207ec4b3fd90ba9991f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb66f4db41478c23128adc14f2796556.png)
(1)求直线l的直角坐标方程及曲线C的普通方程;
(2)证明:直线l和曲线C相交,并求相交弦的长度.
您最近一年使用:0次
2018-10-12更新
|
856次组卷
|
3卷引用:广东省佛山市禅城区2019-2020学年高三上学期统一调研测验(一)文科数学试题
名校
8 . 已知直线
的参数方程为
(
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
,射线
,
分别与曲线
交于
三点(不包括极点
).
(Ⅰ)求证:
;
(Ⅱ)当
时,若
两点在直线
上,求
与
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ea0c89112e34d5096a06165c6cbd015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10adc3992efb2badc23f81d36faa206f.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/925b34a1e7a48f450d883f9a0197e5c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0be5c8e545a1251a276a7726d469f25a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db2388a1c07fdee1a7accfb6882e93c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38335830b93ac4d99c28a8e209eecb3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59fec83a7cecffd20f3fbd85dba6bc4d.png)
(Ⅱ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91950023a67715fe5b61f1c9d1d6f87f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da6b93dbe5272a5167ff4e2918bec864.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
您最近一年使用:0次
2018-03-14更新
|
1106次组卷
|
5卷引用:广东省六校(广州二中,深圳实验,珠海一中,中山纪念,东莞中学,惠州一中)2018届高三下学期第三次联考数学(理)试题
名校
9 . 选修4-4:坐标系与参数方程
在直角坐标系中
中,曲线
的参数方程为
(
为参数),以原点
为极点,
轴的正半轴为极轴建立极坐标系.
(1)写出曲线
的普通方程和极坐标方程;
(2)若直线
与曲线
相交于点
两点,且
,求证:
为定值,并求出这个定值.
在直角坐标系中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7784de0f941caa07cd130c7b63892e4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)写出曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebe1d7c64c601c9d8e2423f4ccec30af.png)
您最近一年使用:0次
2017-02-27更新
|
751次组卷
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2卷引用:2017届广东省深圳市高三下学期第一次调研考试(一模)数学(文)试卷