2024·全国·模拟预测
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,直线
的极坐标方程为
.
(1)求曲线
的极坐标方程;
(2)若直线
与曲线
交于点
,求
的面积.
![](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/25fc915669ba02708fcc28d230355054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.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/b4108a67ccf727ef65b24237c6b4a1f1.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
您最近一年使用:0次
2 . 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,
轴正半轴为极轴建立极坐标系,直线
的极坐标方程为
.
(1)求
的普通方程和
的直角坐标方程;
(2)设直线
与
轴相交于点
,动点
在
上,点
满足
,点
的轨迹为
,试判断曲线
与曲线
是否有公共点.若有公共点,求出其直角坐标;若没有公共点,请说明理由.
![](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/abcd836f0076cf49d2f627dc0e18c59e.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/bc455bd060fcaad68ab763dba95fd579.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)设直线
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d788a8f1a85eda30184e507bb7bd47bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
您最近一年使用:0次
2024-03-27更新
|
1274次组卷
|
10卷引用:四川省广安市2024届高三第二次诊断性考试数学(文)试题
名校
3 . 在直角坐标系中,已知直线
,(
为参数),
为
的倾斜角,
与
轴交于点
,与
轴正半轴交于点
,且
的面积为
.
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4058fc45c49e6710ba7e273cb7888704.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7384b9afcef2d86a87eee0c66f383052.png)
您最近一年使用:0次
2024-01-10更新
|
418次组卷
|
5卷引用:陕西省安康市高新中学、安康中学高新分校2024届高三上学期第二次“尖子生计划”考试理科数学试题
4 . 在平面直角坐标系中,曲线
,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.
(1)求曲线
的极坐标方程;
(2)在极坐标系中,射线
与曲线
分别交于
两点(异于极点
),求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca83a3c2edc7a1d19930fc2dea18b45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc9e0d9cb6cb1dd922db49a434e350f7.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)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9feabc99f62ee569b460e61526e2e.png)
(2)在极坐标系中,射线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cac93b0b1bc6136c9a64c1fce87a4665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9feabc99f62ee569b460e61526e2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
您最近一年使用:0次
2024-01-09更新
|
369次组卷
|
4卷引用:四川省成都市天府新区综合高级中学2024届高三上学期一月考试数学(理)试题
四川省成都市天府新区综合高级中学2024届高三上学期一月考试数学(理)试题四川省成都市天府新区综合高级中学2024届高三上学期一月考试数学(文)试题(已下线)2024年高考数学二轮复习测试卷(全国卷文科专用)西藏林芝市2024届高三一模数学(理)试题
5 . 在直角坐标系
中,已知曲线
(其中
),曲线
(
为参数,
),曲线
(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.
(1)求
的极坐标方程;
(2)若曲线
与
分别交于
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/f749408e6b149aeab39a294538d84800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/061813f1ec633c5c4c393c4de7938322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ae218cdeee9b2dfd2b85297c70146fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fff6e7e2b9f2b68b1647f6350b98dc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3086f4e15ab0b44fa3abc2b3b93bc01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5304b005a1338b2038198c395c406e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9feabc99f62ee569b460e61526e2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
您最近一年使用:0次
2024-01-03更新
|
1018次组卷
|
12卷引用:四川省雅安市2024届高三一模数学(理)试题
6 . 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,
轴非负半轴为极轴建立极坐标系,曲线
的极坐标方程为
.
(1)当
时,求直线
的普通方程;
(2)已知点
,若直线
交曲线
于
两点,且
,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/1fefadb27ee6e521e98e29aecfc3ccee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bc282dae4ac9132196ac5d13f63b901.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/196337705890732e64d41e64e27c5075.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3416881a6f67d05fe6b67787047fc86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d56ab70e602f2e2e291df643ab209162.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/5a907ef7e7c18740a71f95ef8976d4d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
您最近一年使用:0次
2023-12-25更新
|
518次组卷
|
3卷引用:四川省成都市2024届高三一模数学(理)试题
2023·全国·模拟预测
7 . 在直角坐标系xOy中,曲线C的参数方程为
(t为参数).以坐标原点O为极点,x轴正半轴为极轴建立极坐标系,直线l的极坐标方程为
.
(1)求曲线C的普通方程和直线l的直角坐标方程;
(2)过点
作直线l的平行线交曲线C于M,N两点(M在x轴上方),求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f63baf9406aa2d99e6f623d6c6c78511.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13f7d6b2654c7980b29053d513405891.png)
(1)求曲线C的普通方程和直线l的直角坐标方程;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7607c37caa9d8616fe17b154adcb727c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4302b8e9f76aca8454d3df72e80be2bc.png)
您最近一年使用:0次
2023-11-22更新
|
521次组卷
|
3卷引用:2024年普通高等学校招生全国统一考试理科数学领航卷(二)
(已下线)2024年普通高等学校招生全国统一考试理科数学领航卷(二)内蒙古自治区通辽市科尔沁左翼中旗实验高级中学2024届高三上学期12月月考数学(文)试题四川省绵阳市南山中学实验学校2024届高考补习年级二诊模拟数学试题(四)
8 . 在直角坐标系
中,曲线
的参数方程
(
为参数),
是
上的动点,点
是线段
的中点,动点
点的轨迹为曲线
.
(1)求
的参数方程;
(2)在以
为极点,
轴的正半轴为极轴的极坐标系中,射线
与
的异于极点的交点为
,与
的异于极点的交点为
,求
.
![](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/68ad7a6ab7b8d8d094fd41ebcc57b551.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)在以
![](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/b3e186ebc624ebacde9a03b96289f1ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
您最近一年使用:0次
9 . 在平面直角坐标系
中,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
的极坐标方程;
(2)若直线
与曲线
交于
两点,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/132391bcbaeceb6cf81488b817ce3acc.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a657ef2a30276488ba78033ca93a225f.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8a99d2c4a23825f62aadcc40822b5eb.png)
您最近一年使用:0次
2023-10-12更新
|
531次组卷
|
4卷引用:陕西省汉中市2024届高三上学期第二次校际联考模拟预测文科数学试题
陕西省汉中市2024届高三上学期第二次校际联考模拟预测文科数学试题陕西省汉中市2024届高三上学期第二次校际联考模拟预测理科数学试题(已下线)2024年全国高考名校名师联席命制数学(理)信息卷(三)(已下线)2024年全国高考名校名师联席命制数学(文)信息卷(二)
10 . 在平面直角坐标系
中,曲线
的参数方程为
(
为参数),以
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
,曲线
,
相交于
,
两点,曲线
经过变换
后得到曲线
.
(1)求曲线
的普通方程和线段
的长度;
(2)设点
是曲线
上的一个动点,求
的面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7f787a6ffe8b92d33840f0a1d568e49.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/925b34a1e7a48f450d883f9a0197e5c9.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab94459e87c666facddbe1a23ae1899d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f99bcbd5a9e1b3f0e6d54ae44b18fd28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab94459e87c666facddbe1a23ae1899d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
您最近一年使用:0次