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解题方法
1 . 下图所示形如花瓣的曲线
称为四叶玫瑰线,并在极坐标系中,其极坐标方程为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/18/0577ef70-f4b9-47b1-a5ba-08913047f901.png?resizew=180)
(1)若射线
:
与
相交于异于极点
的点
,
与极轴的交点为
,求
;
(2)若
,
为
上的两点,且
,求
面积
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14d7c914fc237caa4bffbadcef16752e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/18/0577ef70-f4b9-47b1-a5ba-08913047f901.png?resizew=180)
(1)若射线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/734a6a1d319648bb969845a9159cdba7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d44e8bc37ed03f44470762748a8f942a.png)
(2)若
![](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/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49a4c11d41372175ba3541a44c3376b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
您最近一年使用:0次
2022-11-14更新
|
1933次组卷
|
5卷引用:宁夏回族自治区银川一中2023届高三三模数学(理)试题
宁夏回族自治区银川一中2023届高三三模数学(理)试题宁夏回族自治区银川一中2023届高三三模数学(文)试题四川省资阳市2022-2023学年高三上学期第一次诊断考试数学(理)试题四川省资阳市2023届高三上学期第一次诊断性考试文科数学试题(已下线)江西省五市九校协作体2023届高三第一次联考文科数学试题变式题21-23
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2 . 如图,在极坐标系Ox中,点
,曲线M是以OA为直径,
为圆心的半圆,点B在曲线M上,四边形OBCD是正方形.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/26/b88ebd87-0bb8-44e6-8aa2-fb3c0699cb56.png?resizew=212)
(1)当
时,求B,C两点的极坐标;
(2)当点B在曲线M上运动时,求D点轨迹的极坐标方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/390df402040b60fed7f448a15d153899.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/26/b88ebd87-0bb8-44e6-8aa2-fb3c0699cb56.png?resizew=212)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56150248dd4b787a2013311e4737e93f.png)
(2)当点B在曲线M上运动时,求D点轨迹的极坐标方程.
您最近一年使用:0次
2022-09-23更新
|
1603次组卷
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9卷引用:宁夏回族自治区银川一中2023届高三第一次模拟考试数学(文)试题
宁夏回族自治区银川一中2023届高三第一次模拟考试数学(文)试题宁夏回族自治区银川一中2023届高三第一次模拟考试数学(理)试题四川省蓉城名校联盟2022-2023学年高三上学期入学联考文科数学试题四川省蓉城名校联盟2022-2023学年高三上学期入学联考理科数学试题河南省南阳市第一中学校2022-2023学年高三上学期第二次月考理科数学试题广西壮族自治区防城港市2023届高三下学期4月月考数学(文)试题(已下线)专题10-1 极坐标与参数方程题型归类(讲+练)-1四川省资中县第二中学2022-2023学年高三上学期11月月考理科数学试题陕西省西安市铁一中学2024届高三上学期月考4数学(理)试题
3 . 以等边三角形的每个顶点为圆心,以其边长为半径,在另两个顶点间作一段圆弧,三段圆弧围成的曲边三角形被称为勒洛三角形,如图,在极坐标系
中,曲边三角形
为勒洛三角形,且
,
,以极点O为直角坐标原点,极轴
为x轴正半轴建立平面直角坐标系
,曲线
的参数方程为
(t为参数).
![](https://img.xkw.com/dksih/QBM/2022/6/2/2992613741322240/2995556340809728/STEM/d3758e8d-6d89-4964-afcf-baefe35bb3a9.png?resizew=155)
(1)求
的极坐标方程和
所在圆
的直角坐标方程;
(2)已知点M的直角坐标为
,曲线
和圆
相交于A,B两点,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3e5af20b2f8c1fba4470f9650989e51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd6c71a0da6a878a5b12bf8a8e784645.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aff004ccf61c3ae95d7f8183cd9740b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a480ba768f87a78e40d443962478f11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3e5af20b2f8c1fba4470f9650989e51.png)
![](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/363f54a5b060e52de378316767920562.png)
![](https://img.xkw.com/dksih/QBM/2022/6/2/2992613741322240/2995556340809728/STEM/d3758e8d-6d89-4964-afcf-baefe35bb3a9.png?resizew=155)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5a6b11637ea396e989ab32d780e745b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/320c0f9263761963de27e41442a62a42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)已知点M的直角坐标为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edaef66a0582e95fb5c57a405acdea9a.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/187663c963598cd7b5ce79d80faac37f.png)
您最近一年使用:0次
2022-06-06更新
|
1243次组卷
|
6卷引用:宁夏银川市六盘山高级中学2023届高三三模数学(理)试题
宁夏银川市六盘山高级中学2023届高三三模数学(理)试题吉林省吉林市普通高中2022届高三第四次调研测试理科数学试题吉林省吉林市普通中学2022届高三下学期第四次调研测试文科数学试题吉林省吉林市2022届高三第四次调研测试数学(理)试题(已下线)专题18 坐标系与参数方程-备战2023年高考数学母题题源解密(全国通用)(已下线)考向45坐标系与参数方程(重点)-1
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4 . 已知直线
:
(
为参数).
(1)当
时,求直线
的斜率;
(2)若
是圆
:
内部一点,
与圆
交于
、
两点,且
,
,
成等比数列,求动点
的轨迹方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a106912c62d48bddb8f9c4eb4c126d24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3416881a6f67d05fe6b67787047fc86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827539d066d1b78e7ef8bc1569864971.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f5d967ad135991b6075ee45df55643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](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/d063ec7f9dbeba72fabf4437f9400e07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f645d4b09fba53f971172cd2602c691.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3ce8eed2660a33465a7f764e76cdba8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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5 . (1)将极坐标
化为直角坐标;将点的直角坐标
化为极坐标.
(2)求曲线
的极坐标方程和曲线
的直角坐标方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/131056c5f04d447eb6c60e9c14969691.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98f93434c97ca8e77f57eef9a862078a.png)
(2)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b979396a703fb14715ba39232f5786a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d567aceed74eeb36098635a6b08a5d7a.png)
您最近一年使用:0次