名校
解题方法
1 . 若直线
(
为参数)与直线
平行,则实数
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af8058f03e19228ecb19030be166bdf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f099c9c499e5844e8aae3cbccf8c7c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd707b69a11f8de5566f23c1a2a9ff5a.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
2 . 在平面直角坐标系
中,以
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)求直线
的一个参数方程;
(2)在极坐标系中,方程
表示曲线
,若直线
与曲线
相交于
,
,
三点,求线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.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/5695b7c8f7f4d6cb7370bf4a8c340894.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)在极坐标系中,方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bef646c712fd8dd11ec827be39be3057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
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3 . 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,
轴正半轴为极轴建立极坐标系,直线
和
的极坐标方程分别为
和
和
与曲线
分别相交于
两点(
两点异于坐标原点).
(1)求
的极坐标方程;
(2)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/c2c4e4f93c2211f5a7bdd51760b7b614.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/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a40d2cf43fce0c99dff3470d554eb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc3f2e3a093c2b85098f01618a8f9661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.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/01c74a907dda6bb7d9d56d009d9df253.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2b83beedb3438153e6f728545fe3e03.png)
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4 . 已知曲线C的参数方程为
(
为参数),直线l的倾斜角为
,且过点
.
(1)求曲线C的普通方程与直线l的参数方程;
(2)若直线l与曲线C交于A,B两点,且
,求直线l的倾斜角
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea24806317e4493a07aab1581cb6fc1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1b6f209d1a805437046ca6ef79dd.png)
(1)求曲线C的普通方程与直线l的参数方程;
(2)若直线l与曲线C交于A,B两点,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dfa5b7e0bfb800aa36baede49f9ad5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
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名校
5 . 圆的极坐标方程是,
则圆的面积是 ( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26b08424923339565eb168438a898420.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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6 . 在平面直角坐标系
中,以
为极点,
轴的正半轴为极轴,建立极坐标系,曲线
和直线
的极坐标方程分别为
和:
.且二者交于
,
两个不同点.
(1)写出曲线
和直线
的直角坐标方程;
(2)若点
的极坐标为
,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/709afd616819d6eaf6a067455ce414ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46080dac27a3ebc9d7b0ecdb181eb18e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(1)写出曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/304c865e1cf97c82fe629d9ef6a5a6cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84a670585856a4db48c9238715156362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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7 . 已知直线
的参数方程为
(
为参数),圆
的极坐标方程为
.
(1)求圆
的直角坐标方程;
(2)设圆
与直线
交于点
,若点
的坐标为
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8efa052746caad1ac92d7f2600063fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4171a30d75286a3e4a1a91f31eba3c40.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设圆
![](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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e96394405807439f8aa1c2edd12a1d47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3979f27823cdcba516dfa885d8afe19d.png)
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名校
解题方法
8 . 如图所示形如花瓣的曲线
称为四叶玫瑰线,在极坐标系中,其极坐标方程为
.
与
相交于异于极点
的点
,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/0a9e1dd70ccd7718f7ede19005034cad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a41d43dcd271ec5d1051e8e898ace03e.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/3f645d4b09fba53f971172cd2602c691.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cecc5906de68f43fc0b54b4f4b93e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
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名校
9 . 在直角坐标系中,曲线
的参数方程
(
为参数),曲线
的参数方程为
(
为参数).以坐标原点为极点,
正半轴为极轴建立极坐标系.
(1)求
的极坐标方程;
(2)设
点的直角坐标为
,直线
经过
点,
交
于点
交
于点
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f698250730ab1810b426b4128c402e07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/163c2b1543189a9971aadbe4a0d11a11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9feabc99f62ee569b460e61526e2e.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7a999c36de5c9a9ce876a4a56fa34c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/705b46b661638b78667cde6482131f74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4570ae4fe3190e1d3533c68e6d68b161.png)
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10 . 平面直角坐标系
中,曲线
的参数方程为
(
为参数),直线
的方程为
,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)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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72f595a6674b1972865cc21200647d32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21d532ce76942846df88c6f66112e50f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb6ea5af4151c003e332a6a619d68a03.png)
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【市级联考】陕西省延安市2019届高三高考模拟试题(一)理科数学2020届河北省部分重点高中高三上学期期末数学(理)试题2020届辽宁省锦州市高三4月质量检测(一模)数学(文)试题2020届辽宁省锦州市高三4月质量检测(一模)数学(理)试题2020届湖南省名师联盟高三上学期第一次模拟数学(理)试题四川省成都市第七中学2023届高考模拟文科数学试题四川省成都市第七中学2023届高三下学期高考模拟数学(文科)试题四川省成都市第七中学2023届高三模拟理科数学试题四川省成都市第七中学2023届高三下学期高考模拟理科数学试题四川省崇州市怀远中学2023届高三适应性考试理科数学试题宁夏银川市第六中学2022-2023学年高二下学期期末考试数学(文)试题宁夏石嘴山市平罗中学2024届高三上学期第一次月考数学(文)试题