名校
1 . 已知直线l经过点
,倾斜角
,设直线l与圆
相交于A,B两点,则点P与A,B两点的距离之积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3c9708ef0dc6d6f5dcf6596d3e4f6e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f96144368b1b5ca55648a797580f022e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f5d967ad135991b6075ee45df55643.png)
A.1 | B.2 | C.![]() | D.4 |
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2 . 在直角坐标系中,以原点为极点,
轴的正半轴为极轴建立坐标系.已知曲线
,过点
的直线
的参数方程为
(
是参数),直线
与曲线
分别交于
,
两点.
(1)写出直线
的普通方程与曲线
的直角坐标方程;
(2)若
,
,
成等比数列,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fee3ed5747742944e9e6d7e3de15da34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38b559f160470e4ae99634b95e2537c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b28d702293147b2c08c374b51834e98a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.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)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17a92b933377ae3453fb36a171c521c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac35b1e8a952aac4f4cdaaf02d868d04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a62cc2e0f761199eab7bd6c9c102e636.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2024-01-08更新
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261次组卷
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2卷引用:宁夏石嘴山市第三中学2016届高考一模数学(文)试题
3 . 以平面直角坐标系的原点为极点,正半轴为极轴,建立极坐标系,两种坐标系中取相同的长度单位,设点A的极坐标为
,直线l过点A且与极轴成角为
,圆C的极坐标方程为
.
(1)写出直线l参数方程,并把圆C的方程化为直角坐标方程;
(2)设直线l与曲线圆C交于B、C两点,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f2137436455816a17f748acd06e7eb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e446bf5189a92b165a80bf32d467572d.png)
(1)写出直线l参数方程,并把圆C的方程化为直角坐标方程;
(2)设直线l与曲线圆C交于B、C两点,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/843363e1d63e1e4b8a6bde5825ef5a4f.png)
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4 . 已知平面直角坐标系xOy的原点和x轴的正半轴分别与极坐标系的极点和极轴重合,直线l的参数方程为
(t为参数),圆的极坐标方程为
,若P,Q分别在直线l和圆上运动,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f8eff1ab04b50a879d5cc8158f49cf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/112d4e39736d9916a2d649f370c65fc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d87446c9ef0230285d9b08127fce5c.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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5 . 已知过定点
的直线
(其中t为参数)与圆
交于M,N两点,则
的中点坐标为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fe413b12ffabfb252121aa2eaa31017.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39ed6c440ccef3a66330dbe7d1a575cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bd59bdc76240a4c5842eb5c6dabff84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
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6 . 直线
是参数
上与点
距离等于4的点Q的坐标为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1b73d17bcee6f0781b83ef739f8412.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7227bb0efef5ecf91f37769f1c4fac19.png)
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解题方法
7 . 直线l过点
,且倾斜角为
,曲线
(θ为参数).
(1)写出直线l的参数方程的标准形式,并求曲线C的普通方程;
(2)若直线l与曲线C交于A,B两点,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f13bf66fc845b115de4ec45b4be0e23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd3b2e58daa2ace0f4071146918d7be5.png)
(1)写出直线l的参数方程的标准形式,并求曲线C的普通方程;
(2)若直线l与曲线C交于A,B两点,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
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8 . 直线
(t为参数)被曲线
截得的弦长为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ef2d0e8e134c89efafa960b981ea059.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e1fa37c4c826b5dcfebe86ab6177906.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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9 . 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
.在平面直角坐标系
中,已知直线
过点
,且倾斜角为
.
(1)求曲线
的直角坐标方程和直线
的参数方程;
(2)设点
的直角坐标为
,直线
与曲线
的交点为
,求
的值.
![](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/87336632fa522b53e317d3e9c4f9a8e9.png)
![](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/fb0e705301752424a492f6277ed7774e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c0927afc571a7c966c98192040979e.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed18bd80c6c4142f68e89f4ad44570b5.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e255cb6ef5a18b9e800397c55a81bf9.png)
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2021-09-11更新
|
479次组卷
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3卷引用:云南省楚雄天人中学2019-2020学年高二5月学习效果监测数学(文)试题
2020高三·全国·专题练习
名校
10 . 在平面直角坐标系
中,直线
的参数方程为
(
为参数).在以坐标原点为极点,
轴的正半轴为极轴的极坐标系中,圆
的极坐标方程为
.
(1)求
的普通方程和圆
的直角坐标方程;
(2)已知点
,直线
与圆
相交于
、
两点,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/b00cbc123f5db989034fea6137a45f20.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aac8a07a96a9091cc9d1f82dd7ad41b5.png)
(1)求
![](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/b1a27281ddfa2f2d69a8bb3e82a66137.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/13c54cd0878ea19f3ae4d35348c04e7f.png)
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2021-01-16更新
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8卷引用:综合练习模拟卷01-2021年高考一轮数学(文)单元复习一遍过
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