2024·全国·模拟预测
名校
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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2 . 在直角坐标系
中,曲线C的参数方程为
(
为参数),直线l的参数方程为
(其中t为参数,
),且直线l和曲线C交于M,N两点.
(1)求曲线C的普通方程及直线l经过的定点P的坐标;
(2)在(1)的条件下,若
,求直线l的普通方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b60b0ad8c8364657a022063b653e5dad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd5673bb0da6fc5d33ac24d20305e5b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10adc3992efb2badc23f81d36faa206f.png)
(1)求曲线C的普通方程及直线l经过的定点P的坐标;
(2)在(1)的条件下,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/167b1af093933472f571690f58ee06f8.png)
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2024-01-14更新
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769次组卷
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6卷引用:陕西省宝鸡市2024届高三上学期高考模拟检测(一)数学(理)试题
3 . 在平面直角坐标系
中,曲线C的参数方程为
(t为参数),以坐标原点O为极点,以x轴正半轴为极轴,建立极坐标系.
(1)求曲线C极坐标方程;
(2)若A,B为曲线C上的动点,且
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e519a71b2bc94d4248f5959c04f1ca4.png)
(1)求曲线C极坐标方程;
(2)若A,B为曲线C上的动点,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acb8956ebcde7cf0f1011a2fc1888e15.png)
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2024-01-13更新
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4卷引用:四川省绵阳市2024届高三二模数学(理)试题
名校
4 . 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)
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2024-01-10更新
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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
2024·全国·模拟预测
5 . 在直角坐标系
中,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.
(1)求
的极坐标方程;
(2)若曲线
的极坐标方程为
,曲线
的极坐标方程为
与
和
的交点分别为
(
异于原点
),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/578e8d6db401bba01636a1c180db288f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f820ed717c9123ef937260b1599fdf48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab94459e87c666facddbe1a23ae1899d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4fd6f664fd18ea5411e108325d68f6a.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/7789a500686c7a73770404ead6af0590.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)
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2024·全国·模拟预测
6 . 在平面直角坐标系xOy中,以坐标原点为极点,
轴正半轴为极轴建立极坐标系,曲线
的极坐标方程是
.
(1)求曲线
的直角坐标方程;
(2)若A,B为曲线
上不同的两点,且满足
,求
的最大值.
![](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/c7f8bbf5ba89608b848ee873ec728c9a.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若A,B为曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac51bffb8f476896081027b33f7ec25d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37b337c93f29459c8f59a0e1cf2d94e3.png)
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2024·全国·模拟预测
7 . 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)写出直线
的直角坐标方程与曲线
的普通方程;
(2)过点
且与直线
平行的直线
与曲线
相交于
两点,与
轴相交于点
,求
的值.
![](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/919d7c3a6c20104dafe3e2da2102a43a.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a4f7224c5be14018340f3222b4d1429.png)
(1)写出直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fdf0b6fecd6a78bc83f42e11e60a004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfd193389f32df0162b77e7de4a41e28.png)
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名校
8 . 在直角坐标系
中,曲线
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,直线
的极坐标方程
.
(1)求
和
的直角坐标方程;
(2)直线
与C交于MN两点,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/35d898de3e32d7cd0cea11e5e3eb7581.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18baf286c139692f7482b4f72dcf4447.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dd698d57d1cf239eb8752aecaaa4f4.png)
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2024-01-05更新
|
568次组卷
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2卷引用:广东省广州市从化中学2020届高三上学期第三次月考数学(理)试题
9 . 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)
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2024-01-03更新
|
1018次组卷
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12卷引用:四川省雅安市2024届高三一模数学(理)试题
10 . 在直角坐标系中,曲线
的参数方程为
;在极坐标系(以原点为坐标原点,以轴正半轴为极轴)中曲线
的方程为
,则
与
的交点的距离为__________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d8a231125afc3eb4eed9bcc65213a5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76817e4d13d29c0644a6286a1f9e22ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
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