2024·全国·模拟预测
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1 . 在平面直角坐标系xOy中,曲线C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C的极坐标方程;
(2)若点
,
,
都在曲线C上,求
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbd494adc8e1ca5cc8613069218f97c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
(1)求曲线C的极坐标方程;
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81e5094ea2e1ae387f33e0b554c60b14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/567d460332abe9f84dec7bffd68723ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6d8696798d9553916455bd8fe15d747.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
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解题方法
2 . 如图,在极坐标系
中,圆
的半径为
,半径均为
的两个半圆弧
所在圆的圆心分别为
,
,
是半圆弧
上的一个动点,
是半圆弧
上的一个动点.
(1)若
,求点
的极坐标;
(2)若点
是射线
与圆
的交点,求
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3e5af20b2f8c1fba4470f9650989e51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9feabc99f62ee569b460e61526e2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b859e308fcce9f40cf7bf0fa3a717f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3449cf3f7f863c11344d3f53805062ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/7/3bf255b5-d7e6-4bb0-b821-96064fe9a497.png?resizew=163)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bb74037b00cf71e49dae1663a2abb47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65125a43aa50b652de8f5614b81f176a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/893de44d87d91b0508165c2b6edaed79.png)
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|
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10卷引用:江西省景德镇市2023届高三第三次质量检测理科数学试题
江西省景德镇市2023届高三第三次质量检测理科数学试题江西省景德镇市2023届高三第三次质量检测文科数学试题宁夏回族自治区银川一中2024届高三上学期第二次月考数学(理)试题宁夏回族自治区银川一中2024届高三上学期第二次月考数学(文)试题四川省绵阳中学2023-2024学年高三上学期一诊模拟(三)数学(理科)试题四川省绵阳市三台中学校2023-2024学年高三上学期第二学月测试理科数学试题四川省泸州市泸州老窖天府中学2024届高三一模数学(文)试题(二)四川省泸州市泸州老窖天府中学2024届高三上学期数学(理科)一诊模拟(二)试题(已下线)2024年全国高考名校名师联席命制数学(理)信息卷(八)(已下线)2024年全国高考名校名师联席命制数学(文)信息卷(八)
3 . 在平面直角坐标系
中,已知直线
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,曲线
的极坐标方程为
.
(1)求曲线
的直角坐标方程;
(2)若直线
与曲线
相切,求直线
的斜率.
![](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/72556f17afa4295539c4333727c8b684.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/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c06f75ac445f6fb9e309942f144dd81f.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)若直线
![](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/0f85fca60a11e1af2bf50138d0e3fe62.png)
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2023-09-04更新
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2卷引用:江西省赣州市兴国县联考2023届高三下学期5月月考文科数学试题
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4 . 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
为直角坐标原点,极轴
为
轴正半轴建立平面直角坐标系
,曲线
的参数方程为
(
为参数).
(1)求
所在圆
的直角坐标方程;
(2)已知点
的直角坐标为
,曲线
和圆
相交于
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/38006dd796744ebf4470424e9fdb9515.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3e5af20b2f8c1fba4470f9650989e51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/23/167fe45a-3625-4439-a86e-78abda7e82e6.png?resizew=145)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/320c0f9263761963de27e41442a62a42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3371afe42800f23fd9b933d6e4f5c56.png)
您最近一年使用:0次
5 . 在直角坐标系xOy中,直线l的方程为
.以坐标原点O为极点,x轴正半轴为极轴建立极坐标系,已知曲线
的极坐标方程为
,曲线
的参数方程为
.
(1)求曲线
的直角坐标方程;
(2)若
为曲线
上第一象限的动点,A,B分别为曲线
与直角坐标轴正半轴的交点,求四边形OAQB面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30d0bf7a4c131a9c7de0a2db3b11e992.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcdebedd02b4ea57f8562443742086d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83c66e1c7a55766c4bbf9f32e6047d.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b3cb96f78ec5153e97ba299e8d18ac5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
您最近一年使用:0次
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6 . 在平面直角坐标系xOy中,直线
的参数方程为
(
为参数),以O为极点,
轴的正半轴为极轴建立极坐标系,曲线C的极坐标方程为
.
(1)求C的直角坐标方程以及C与y轴交点的极坐标;
(2)若直线
与C交于点A,B,与
轴交于点P,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53f015d2ddf2146636a2f7565a380112.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/9bec39a5f5021d0b06208814334e6c63.png)
(1)求C的直角坐标方程以及C与y轴交点的极坐标;
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7384b9afcef2d86a87eee0c66f383052.png)
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2023-05-26更新
|
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7卷引用:江西省南昌市部分学校2023届高三模拟考前押题模拟预测数学(理)试题
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7 . 在直角坐标系xOy中,圆C的参数方程为
为参数),以O为极点,x轴正半轴为极轴建立极坐标系.
(1)求圆C的极坐标方程;
(2)AB是圆C上的两点,且∠AOB=
,求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb01cf0dbc9941a7e217eb13976c9cdd.png)
(1)求圆C的极坐标方程;
(2)AB是圆C上的两点,且∠AOB=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
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2023-05-25更新
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6卷引用:江西省稳派联考2023届高三模拟预测数学(理)试题
8 . 在直角坐标系
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
的普通方程和直线
的直角坐标方程;
(2)已知点
的极坐标为
,设曲线
和直线
交于M,N两点,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/0506efc4984a3873a2b18ab8b816e119.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/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aadf5085d28cc1907231baa8ec53f787.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bace556de6191e2e3277f7772f7c3947.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/f9b57ecee5f1eaa2fa61f09820fbbac1.png)
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2023-05-17更新
|
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2卷引用:江西省新八校2023届高三第二次联考数学(文)试题
9 . 在极坐标系中,圆
的极坐标方程为
,直线
的极坐标方程为
. 以极点为坐标原点,以极轴为
轴的正半轴,建立平面直角坐标系
.
(1)求圆
及直线
的直角坐标方程;
(2)若射线
分别与圆
和直线
交于
两点,其中
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18c16adcdf3d36f9efeb4fe9a4944ca5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7758d5da1694c922090cbd519a7ad3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)若射线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdf0ebb75a4215fc704663984af206c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dcbe8b4bcd32e5a64ebfd873f8cbb2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3b4394cae20185821fadfced2c5118b.png)
您最近一年使用:0次
10 . 在平面直角坐标系
中,直线
的参数方程为
(t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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35097824f3ec45d6bdf4092956412e2b.png)
(1)求曲线C的直角坐标方程和直线l的普通方程;
(2)若
与C交于M,N两点,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/88a38dba8925a1d010cb9bc4f3c90295.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35097824f3ec45d6bdf4092956412e2b.png)
(1)求曲线C的直角坐标方程和直线l的普通方程;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84e4c652fd34eb7de9dbf84d92c6e640.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77684b3856f797403b2040c5dc73c2ce.png)
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2023-05-12更新
|
495次组卷
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3卷引用:江西省抚州市金溪县2023届高三高考仿真模拟考试数学(文)试题