名校
1 . 在直角坐标系
中,已知曲线
(
为参数),在极坐标系中,曲线
是以
为圆心且过极点
的圆.
(1)分别写出曲线
普通方程和曲线
的极坐标方程;
(2)直线
与曲线
、
分别交于
、
两点(异于极点
),求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a28ccba5981ff469c05f7fcc48897474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97e967ff5c1c3bc20a29e3cfce1e374.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(1)分别写出曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efbf5c22e89f0b2c1a93dbb2bf3eb015.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/084cf5ffced059f5653ee2a1023518b7.png)
您最近一年使用:0次
2023-08-03更新
|
270次组卷
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7卷引用:广西玉林市北流市2023届高三年级教学质量检测数学(理)试题
2 . 曲线
的参数方程为:
,
为参数.以原点为极点,
轴正半轴为极轴建立极坐标系,直线
的方程为
.
(1)求曲线
的普通方程和极坐标方程.
(2)若直线
与曲线
相交于点A,点B在圆
:
上,求
的最小值及此时的
值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/040c52750f7133583850305ee063b471.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17f5d2e8186f0173d7862b1d39fb3dc2.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63b8e68713c34c549d9b841d35322eca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
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名校
3 . 在直角坐标系xOy中,曲线
的参数方程为
(t为参数且
),
分别与x轴、y轴交于A、B两点.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,曲线
的极坐标方程为
.
(1)
与坐标轴交于A,B两点,求
;
(2)求
上的点到直线AB距离的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e8751d60072368150728b384aa48ce6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a369ce3949b2bd2747a48054f7b951c4.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/9b4c7a1116fa778512168b6b5b99ae24.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
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2023-05-12更新
|
762次组卷
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2卷引用:广西南宁市第三中学2023届高三一模测试数学(理)试题
解题方法
4 . 已知曲线
的参数方程是
(
是参数),以坐标原点为极点,
轴的非负半轴为极轴建立极坐标系.
(1)写出曲线
的极坐标方程;
(2)若点
,
,
在曲线
上,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13ddb104406e14773c9cc60bda30c91b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)写出曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/299e193c0bb7580f2e0a6f122634f098.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc05578fbe4e91c91900dea4c50f5f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05211187f61de40869dd0c5b0b5e9c4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0f353bf37e83b723b3b74821feb91db.png)
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2023-05-03更新
|
121次组卷
|
2卷引用:广西邕衡金卷2023届高三一轮复习诊断性联考数学(理)试题
名校
5 . 在平面直角坐标系
中,已知曲线
的参数方程为
(
为参数),以原点
为极点,
轴正半轴为极轴建立极坐标系.
(1)求曲线
的极坐标方程;
(2)设射线
和射线
分别与曲线
交于
、
两点,求
面积的最大值.
![](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/e98121fbf4c95d9fc07bf9df9875f219.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)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设射线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bd54574fa77e01a57fc7762a2664ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fe7391aff4de6f355ada96be4badc69.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
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2023-03-29更新
|
1658次组卷
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17卷引用:广西柳州市2023届高三第三次模拟数学(文)试题
广西柳州市2023届高三第三次模拟数学(文)试题广西柳州市2023届高三第三次模拟数学(理)试题广西壮族自治区南宁市武鸣区武鸣高级中学2023届高三二模理科数学试题贵州省六校联盟2023届高三上学期高考实用性联考卷(二)数学(文)试题贵州省六校联盟2023届高三上学期高考实用性联考卷(二)数学(理)试题(已下线)易错点17 极坐标和参数方程四川省成都市石室中学2023届高三下学期高考专家联测卷(四)数学(理)试题四川省成都市石室中学2023届高三下学期高考专家联测卷(四)数学(文)试题四川省绵阳实验高级中学2023届高三第6次模拟测试理科数学试题四川省乐山市2023届高三三模理科数学试题四川省泸州市2023届高三三摸文科数学试题陕西省联盟学校2023届高三下学期第三次大联考理科数学试题江西省上饶一中、上饶中学2023届高三高考仿真模拟数学(文)试题四川省绵阳南山中学2022-2023学年高二下学期期末热身考试数学(理)试题陕西省联盟学校2023届高三第三次大联考数学(文)试题四川省泸州市2023届高三三模理科数学试题四川省绵阳中学2023届高三适应性考试(三)理科数学试题
名校
6 . 在直角坐标系
中,以坐标原点为极点,x轴非负半轴为极轴建立极坐标系,曲线C的极坐标方程为
,其中
为参数.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/19/551a520a-4a56-4bc9-a4ad-acd5e94aa6aa.png?resizew=150)
(1)求曲线C的直角坐标方程,并画出曲线C的简图(无需写出作图过程);
(2)直线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faf4ec21e5682d3f0c3bd3485a1bbf4e.png)
与曲线C相交于A,B两点,且
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcd0ca66a1e11ad8008e8f6c8a18ba15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/19/551a520a-4a56-4bc9-a4ad-acd5e94aa6aa.png?resizew=150)
(1)求曲线C的直角坐标方程,并画出曲线C的简图(无需写出作图过程);
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faf4ec21e5682d3f0c3bd3485a1bbf4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b153c717bf297548ac393b1e9448dcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/631586067d81160678c2ddea983e62de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
您最近一年使用:0次
名校
解题方法
7 . 如图,在极坐标系中,曲线
是以
为圆心的半圆,曲线
是以
为圆心的圆,曲线
都过极点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/16/8435dbf9-096f-43d6-b1a2-2971ce3ff8c6.png?resizew=215)
(1)分别写出半圆
,圆
的极坐标方程;
(2)直线
与曲线
分别交于
两点(异于极点
),求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7bb4641b79fde549b29358e8c03b60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/314eade91ed52f71eaef46dec2465179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/880248fa1259b2600a87f09a61287d44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/16/8435dbf9-096f-43d6-b1a2-2971ce3ff8c6.png?resizew=215)
(1)分别写出半圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55115ae4e0f684a3ff0acda7a3afa6c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9feabc99f62ee569b460e61526e2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86e203b7c9a6600e0272c58a23733490.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8de295f97af2786de1492c58397b6a94.png)
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2023-03-16更新
|
823次组卷
|
4卷引用:广西壮族自治区桂林市、河池市、防城港市2022-2023学年高三联合调研考试数学(文)试题
广西壮族自治区桂林市、河池市、防城港市2022-2023学年高三联合调研考试数学(文)试题广西壮族自治区桂林市等2地2023届高三下学期3月月考数学(理)试题(已下线)专题10-1 极坐标与参数方程题型归类(讲+练)-1宁夏银川市第二中学2024届高三上学期年级统练四数学(理)试题
解题方法
8 . 在直角坐标系
中,曲线
(
为参数,
)其中
,在以
为极点,
轴正半轴为极轴的极坐标系中,曲线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46a0e4124d4d6696fd068c990536f2f7.png)
(1)求曲线
的极坐标方程;
(2)若
与
相交于点
,
与
相交于点
,求
的最大值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7fc6a3cb8bb9c7624228a71f8495925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/823ab696d27d40920c39b8c910789380.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76c516619a5b3c6676e6734efa754e5d.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/46a0e4124d4d6696fd068c990536f2f7.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)若
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab94459e87c666facddbe1a23ae1899d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
9 . 在直角坐标系
中,曲线
的参数方程为
(t为参数),曲线
的参数方程为
(
为参数).以坐标原点为极点,x轴正半轴为极轴建立极坐标系.
(1)求曲线
的极坐标方程与
的普通方程;
(2)若直线
与曲线
交于A点、与曲线
交于B点,求
的值.
![](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/b7ffbb2eeccc5ecfb999044cbe7ab2f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d2cb50b2abb7359a3bd0fe104743411.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a40d2cf43fce0c99dff3470d554eb8.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/aaff41080fdea43eea7efedf9ebc1498.png)
您最近一年使用:0次
解题方法
10 . 在平面直角坐标系
中,已知曲线
的参数方程为
(
为参数).以坐标原点为极点
轴正半轴为极轴建立极坐标系,直线
的参数为
(
为参数).
(1)求曲线
和直线
的直角坐标方程;
(2)过原点
引一条射线分别交曲线
和直线
于
、
两点,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce1132157a33c82610c2d5035493d024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f09b9a2ea4f4dfbe5f81857aa214c7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07c9121cede0ee0562e23b8a26b34616.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ffb694021b52653de5141ae27ba6d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a159de0b2d9eb1ae0b7e664e64d3c6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8edfa16cd6adb98872c604f0e413b09a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08075b3b73dd2609baad69a496fdd9a8.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce1132157a33c82610c2d5035493d024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a159de0b2d9eb1ae0b7e664e64d3c6c.png)
(2)过原点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/701f3b0e2bedfe5195443459072d798e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce1132157a33c82610c2d5035493d024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a159de0b2d9eb1ae0b7e664e64d3c6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0914b68f106a912420705b2f3928ca42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da9dcf6c319174c9ea2b1ceaed1649a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd5edf32d6eb1aa719a91ffb02d23ac1.png)
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2022-10-19更新
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4卷引用:广西2022届高三高考桂柳鸿图综合模拟金卷(2)数学(文)试题