1 . 以直角坐标系的原点0为极点,轴的正半轴为极轴建立极坐标系,已知点P的直角坐标为(1,
),点M的极坐标为(2,
),若直线l过点P,且倾斜角为
,圆M的半径为2.
(1)求直线l的参数方程(写出一个即可)和圆M的极坐标方程;
(2)设直线l与圆M相交于A,B两点,求
的值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ad72d7565699d1ebb741eb0ce12bac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f785147690f83dcee0a0bc6c327e75a.png)
(1)求直线l的参数方程(写出一个即可)和圆M的极坐标方程;
(2)设直线l与圆M相交于A,B两点,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97734ea5ad4e80562025b1a1621e2823.png)
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2卷引用:广西玉林市第十一中学2021届高三下学期高考热身考试数学(文)试题
2 . 已知曲线
的参数方程为
(
为参数).
(1)求曲线
的普通方程;
(2)过点
的直线
与曲线
交于
,
两点,求|PA|•|PB|的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba3d738828366d624fda3565a86dc142.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1b6f209d1a805437046ca6ef79dd.png)
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
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3 . 在直角坐标系
中,点
是曲线
:
上的动点,满足
的点
的轨迹是
.
(1)以坐标原点
为极点,
轴的正半轴为极轴建立极坐标系,求曲线
,
的极坐标方程;
(2)直线
的参数方程是
(
为参数),点
的直角坐标是
,若直线
与曲线
交于
,
两点,当线段
,
,
成等比数列时,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.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/8bac4d3d2be66e9f25b59e3a94f235e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eec446f3a2fac01d5248eb647307fd7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(1)以坐标原点
![](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/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d2a96aadf335a8f41365e0639358b48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a2a5e336b6bcba6354fd366c892dd06.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d341082cc54b1cb7a790af9ec4a365d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/084cf5ffced059f5653ee2a1023518b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18e49c41a2ee9a447d67f8e726a73460.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d66c03d4ca06819a6ce7fc8ea6de0f0.png)
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8卷引用:甘肃省2021届第二次高考诊断理科数学试题
4 . 已知直线l的参数方程是
(
,
为参数),则直线l的倾斜角的大小为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3d4f07fae0375ea02fc7b294a78fd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dcbca3478eae63853d2aab5332e2e56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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5卷引用:上海市普陀区2021届高三下学期高考调研数学试题
上海市普陀区2021届高三下学期高考调研数学试题(已下线)专题11 坐标系与参数方程-2021年高考真题和模拟题数学(文)分项汇编(全国通用)(已下线)第1-2章 直线与圆(附加篇:参数方程)(单元培优)-2021-2022学年高二数学课后培优练(苏教版2019选择性必修第一册)(已下线)考向31 坐标系与参数方程-备战2022年高考数学一轮复习考点微专题(上海专用)(已下线)专题14 参数方程与极坐标方程-备战2022年高考数学(文)母题题源解密(全国乙卷)
5 . 在直角坐标系
中,点
为坐标原点,直线
的直角坐标方程为
,直线
与x轴交于点M,抛物线C的参数方程为
(
为参数).
(1)以点O为极点,以
轴正半轴为极轴,求直线
的极坐标方程及点M的极坐标;
(2)设直线
与抛物线C相交于E,F两点,若
,求抛物线C的准线方程.
![](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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4b4c7dc317e98b9305f8f85ab62058.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d8fd882c41b70029edda3c3a9e674d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/121c8e731e8cd318e60ee5b1d07638b1.png)
(1)以点O为极点,以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/9f5ce17af3d6e0b4f0cfe2304711d419.png)
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2卷引用:四川省天府名校2021届高三5月诊断性考试理科数学试题
6 . 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,曲线
的极坐标方程为
.
(1)求直线
的普通方程与曲线
的直角坐标方程;
(2)已知点
的直角坐标为
,过点
作直线
的垂线
交曲线
于
、
两点(
在
轴上方),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/dea37afdde5db0f1649fad958fa2ecdf.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/00999b9a5320bad39b04ad762aa71a0a.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fab8a0cc6504aa4c3a38006f5394b4c2.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/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd2474de866ffdd868647a232da193c.png)
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5卷引用:黑龙江省哈尔滨市第三中学2021届高三第四次模拟考试数学(文)试题
名校
7 . 在直角坐标系
中,以坐标原点为极点,以
轴正半轴为极轴,建立极坐标系,直线
的极坐标方程
,曲线C的极坐标方程为
.
(1)写出直线
和曲线C的直角坐标方程;
(2)已知点
,若直线
与曲C线交于P、Q两点,PQ中点为M,求
的值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.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/0454f6f4366f3618dc1ec322ec78e50d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e7f40f7eb906249ffb2a29cef9f533d.png)
(1)写出直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8748dc55e2f45bc37fc4d84d7310f79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d9ff510a25cef7b19ba0c4ae5ea3ef2.png)
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2021-05-20更新
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6卷引用:河南省郑州市2021届高三三模文科数学试题
8 . 平面直角坐标系
中,直线
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
的极坐标方程是:
.
(Ⅰ)求
的直角坐标方程和
的普通方程;
(Ⅱ)设
,
与
交于
,
两点,
为
的中点,求
.
![](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/39894a22c1ef467bc1163c01834dfaad.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/442ff84284c62c591a30c742c5cf47b0.png)
(Ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(Ⅱ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1b6f209d1a805437046ca6ef79dd.png)
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d341082cc54b1cb7a790af9ec4a365d.png)
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8卷引用:黑龙江省哈尔滨师范大学附属中学2021届高三第三次模拟文科数学试题
9 . 平面直角坐标系
中,曲线C的参数方程为
(
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,直线l的极坐标方程为
.
(1)写出曲线C的普通方程和直线l的直角坐标方程;
(2)若直线l与曲线C交于P,Q两点,点
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/950b7d4336130e7c7a1b02f0e90c77bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2725a89d93c791f7a0098f4964587905.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b0aad328f5ad3e07a64e858f49d1ca6.png)
(1)写出曲线C的普通方程和直线l的直角坐标方程;
(2)若直线l与曲线C交于P,Q两点,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b25ce60648ea5042ab5eb5702efe651a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e007d5f2d0c7a5f1f0abaa6dfba27cee.png)
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2021-05-12更新
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2卷引用:四川省攀枝花市2021届高三二模考试数学(文)试题
10 . 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
与直线
的普通方程;
(2)设直线
与曲线
相交于
,
两点,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/17f33ba96b4c6c7d059384ccbbf6aa55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.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/17c3812c12714bf01c0f57e7bb7ebf75.png)
(1)求曲线
![](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/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/f1ff2f3aa2e61188e940fe23ca9aa1e7.png)
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2021-05-11更新
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2卷引用:四川省成都市2021届高三三模数学(理科)试题