名校
1 . 在极坐标系中,点
与
之间的距离为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96503ebb0897ebb31fcd9c2423e71e33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dbc67ea02a760a64f4a57dea9b7a3b0.png)
A.1 | B.2 | C.3 | D.4 |
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9卷引用:河北省邢台市第八中学2018-2019学年高二下学期期末数学(文)试题
河北省邢台市第八中学2018-2019学年高二下学期期末数学(文)试题河北省邢台市第八中学2018-2019学年高二下学期期末数学(理)试题黑龙江省伊春市伊美区第二中学2019-2020学年高二上学期期末考试数学(文)试题山西省应县第一中学校2021届高三上学期开学考试(高二下学期期末)数学(理)试题沪教版(2020) 选修第一册 新课改一课一练 期中测试C河南省郑州市励德双语学校2021-2022学年高二下学期第一次月考数学(文)试题黑龙江省大庆实验中学2019-2020学年高二下学期第五次网上周测数学(理)试题西藏自治区林芝市第二中学2019-2020学年高二下学期第一次月考数学(文科)试题江西省赣州市八校协作体2020-2021学年高二下学期期中联考数学(文)试题
2 . 已知在平面直角坐标系
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
的极坐标方程以及直线
的直角坐标方程;
(2)已知点
在曲线
上,点
在直线
上,若直线
与直线
所成的角为
,求
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/0e2c0691a6b59461c05f56d44a12606c.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f83867c42b457c164c2f2d59afbf2380.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)已知点
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d063ec7f9dbeba72fabf4437f9400e07.png)
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2卷引用:华大新高考联盟2023-2024学年高三上学期11月教学质量测评理科数学试题
3 . 在平面直角坐标系
中,已知直线
的参数方程为
(
为参数),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
.
(1)求直线
的普通方程和曲线
的直角坐标方程;
(2)在直角坐标系中,若把曲线
图象向下平移
个单位,然后横坐标不变,纵坐标压缩到原来的
,得到曲线
,直线
与曲线
交于点
、
,与
轴交于点
,求
的值.
![](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/a9017a9969c403f23412f3ee7c60d17e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.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/69cf89e94eb51129f144d9809ec290f7.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)在直角坐标系中,若把曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77684b3856f797403b2040c5dc73c2ce.png)
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4卷引用:“四省八校”2021-2022学年高三上学期期中质量检测考试文科数学试题
“四省八校”2021-2022学年高三上学期期中质量检测考试文科数学试题(已下线)专题十一 能力提升检测卷 (测) — 2022年高考数学一轮复习讲练测(课标全国版)宁夏银川一中、昆明一中2023届高三联合二模考试数学(文)试题宁夏银川一中、昆明一中2023届高三联合二模考试数学(理)试题
解题方法
4 . 若直线
(
为参数)与曲线
(
为参数)的交点个数是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf477e65084f00defaa87a952ab34378.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db18903e6c7682a1cba7d8aa12ca6715.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
A.2 | B.1 | C.0 | D.不确定 |
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3卷引用:上海市上海大学附属中学2019-2020学年高二上学期期末数学试题
名校
5 . 若
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/769e18bf39233f4fd608a1caf492979e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b323ce17f06aa04dd45d69cc38b3cac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88bee8e70f1fab639be1636c7bce0477.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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4卷引用:宁夏银川市第二中学2021-2022学年高二下学期期中考试数学(文)试题
宁夏银川市第二中学2021-2022学年高二下学期期中考试数学(文)试题四川省南充市白塔中学2022-2023学年高三上学期入学考试数学(理)试题四川省南充市白塔中学2022-2023学年高三上学期入学考试数学(文)试题(已下线)高二上学期期中【夯实基础60题考点专练】(选修一全部内容)-2022-2023学年高二数学考试满分全攻略(人教A版2019选修第一册)
6 . 已知曲线
的参数方程
(
为参数,且
).若以下曲线中有一个是
,则曲线
是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7631b1e6f596c90a512396809bff427.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907a344929dd28678993b4d3d6f9550a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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3卷引用:河南省郑州市2020-2021学年高二下学期期末数学文科试题
名校
7 . 点M的直角坐标为
,则点M的一个极坐标为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc85c6996aa204ca211c688b1c6da049.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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|
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6卷引用:华中师范大学第一附属中学2018-2019学年高二上学期期中检测理科数学试题
8 . 已知极坐标系的极点在平面直角坐标系的原点
处,极轴与
轴的非负半轴重合,且长度单位相同,直线
的极坐标方程为
,曲线
(
为参数).其中
.
(1)试写出直线
的直角坐标方程及曲线
的普通方程;
(2)若点
为曲线
上的动点,求点
到直线
距离的最大值.
![](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/2264b1ab69bece74eef77f7832b3c0c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3679cad43927e1adbd8cc3c14a88be33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/478d78848ca1be76aa5dfb2df2dbecd0.png)
(1)试写出直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若点
![](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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2018-03-09更新
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5卷引用:江西上饶市2018届高三上学期第一次模拟考试数学(理)试题
9 . 已知极坐标系的极点与直角坐标系的原点O重合,极轴与x轴的正半轴重合,若直线l的参数方程:
(t为参数),曲线C的极坐标方程为:
.
(1)求直线l的普通方程和曲线C的直角坐标方程;
(2)求直线l被曲线C截得线段的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e77219b1e8b89402aeff5495baa95e07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c443aeb0b35096f4d9cfb397086083b2.png)
(1)求直线l的普通方程和曲线C的直角坐标方程;
(2)求直线l被曲线C截得线段的长.
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3卷引用:【全国市级联考】江苏省宿迁市2017-2018学年高二下学期期末考试数学(理)试题
10-11高二下·辽宁·期中
10 . 已知直线
(
为参数),圆
(
为参数).
(Ⅰ)当
时,试判断直线
与圆
的位置关系;
(Ⅱ)若直线
与圆
截得的弦长为1,求直线
的普通方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4abbdd69b98743c3d0a05ad9ef2f10ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ea83b5fc244678edbb1aca8a335459a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(Ⅰ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c95fa7f61564978c8e26616bc14449e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(Ⅱ)若直线
![](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/0f85fca60a11e1af2bf50138d0e3fe62.png)
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