1 . 在平面直角坐标系xOy中,曲线C的参数方程为
,(
为参数),以原点O为极点,x轴的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)已知点
,直线l与曲线C交于A,B两点,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d791cad657b4327c56dc1c1bc177c72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95f5d854ff2fc5146a6450802cfa1623.png)
(1)求曲线C的普通方程和直线l的直角坐标方程;
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33cc0f9aa168e43cc5759f017d69b498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7384b9afcef2d86a87eee0c66f383052.png)
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3卷引用:西南四省名校2022届高三下学期第三次大联考理科数学试题
2 . 在直角坐标系xOy中,直线l的参数方程为
(t为参数,
),曲线C的参数方程为
(
为参数,
),以坐标原点为极点,x轴的正半轴为极轴建立极坐标系.
(1)求曲线C的极坐标方程;
(2)设直线l与x轴交于点P,与曲线C交于两点A,B.求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71ac10ec0f5c9715280c48430d9ed15c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76c516619a5b3c6676e6734efa754e5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0358f447dde1e70052e2e23a298e02da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c1592e2f4c18943d1c5321959d1801f.png)
(1)求曲线C的极坐标方程;
(2)设直线l与x轴交于点P,与曲线C交于两点A,B.求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01db917a6fa38b67551cf2d911a1dd76.png)
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3 . 在平面直角坐标系中,已知直线
的参数方程为
(
为参数),曲线
的方程为
.以坐标原点
的极点,
轴的正半轴为极轴建立极坐标系.
(1)求直线
及曲线
的极坐标方程;
(2)设直线
与曲线
相交于
,
两点,满足
,求直线
的斜率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1eb71edf8424b30fd942f5316cdad638.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/3195068f0f90eaf85e9960b284a32c5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edca3d7bb2baca68fbc19be37ac1ca2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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4 . 已知曲线
为参数
,
为参数
.
(1)求
的普通方程;
(2)若
上的点
对应的参数为
,
为
上一个动点,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec1cc0fdbadd5fb64699238b18c55bad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34ad4b2044bc681e2c0b17d0261aa703.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9feabc99f62ee569b460e61526e2e.png)
(2)若
![](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/118904a3295c9679231bab4f29430ea4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d44e8bc37ed03f44470762748a8f942a.png)
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4卷引用:陕西省安康市2022届高三下学期第二次教学质量联考理科数学试题
名校
5 . 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,x轴的非负半轴为极轴建立极坐标系,射线l的极坐标方程为
,将射线l绕点逆时针旋转
后,得到射线
,若射线l,
分别与曲线C相交于点A,点B.
(1)求曲线C的极坐标方程;
(2)求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03c546d0938e6c3e2969bbb495512427.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42c5cc685af04307edca33ff0b56c444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ad72d7565699d1ebb741eb0ce12bac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
(1)求曲线C的极坐标方程;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff24c95fe581befd56c3bcc70e88b726.png)
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名校
6 . 在直角坐标系
中,以坐标原点为极点,x轴正半轴为极轴建立极坐标系,曲线C的极坐标方程为
.
(1)将C的极坐标方程化为直角坐标方程;
(2)为解决倍立方体问题,数学家引用了蔓叶线.设M为C上的动点,M关于
的对称点为N(M、N不与原点重合),M在x轴的射影为H,直线
与直线
的交点为P,点P的轨迹就是蔓叶线.请写出P的轨迹的参数方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e0cb878349009a779d94b1bc40319bb.png)
(1)将C的极坐标方程化为直角坐标方程;
(2)为解决倍立方体问题,数学家引用了蔓叶线.设M为C上的动点,M关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88e9f7d1272b7344346b58b660aa260a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83042953e7f15e984b2da2ee9ca678d1.png)
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解题方法
7 . 若直线l的参数方程为
(t为参数),则直线l的倾斜角的大小为____________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/133175cfb2e632875a8d4fa8ed52591b.png)
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8 . 在直角坐标系
中,曲线
的方程为
.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
,其中
为常数且
.
(1)求直线
的普通方程与曲线
的极坐标方程;
(2)若直线
与曲线
相交于
两点,求
的取值范围.
![](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/9f99b71bea536a435f558d319e9af1eb.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/bcdbf97b29f90d1a5c001b98f90b0071.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e6b60aec15207d0c144c94f2ec428c2.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](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/37b337c93f29459c8f59a0e1cf2d94e3.png)
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2022-03-22更新
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3卷引用:四川省成都市2022届高三第二次诊断性检测文科数学试题
名校
解题方法
9 . “曼哈顿距离”是由赫尔曼闵可夫斯基所创的词汇,是一种使用在几何度量空间的几何学用语,例如在平面直角坐标系中,点
,
、
,
的曼哈顿距离为:
.若点
,点
为圆
上一动点,则
的最大值为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/033ccd1ebf578e1727d7907379fa828a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a350eb41c3b7e4face9c3299eff9d49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66e3c5d2e75308c341c6ddda9402eb64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24529eadaef974ec0625f8ca40682e51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2a60483e0456f3ebbb5c969ff660e3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dbcf0320d94734aedd3d4e2e31b9827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9ab11ba6b230c4309e1b899eb58daae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/135b08696706de37e1eab5f59697674c.png)
您最近一年使用:0次
10 . 在平面直角坐标系
中,直线
的方程为
;以
为极点,
轴的正半轴为极轴建立极坐标系,且曲线
的极坐标方程为
.
(1)求
的直角坐标方程和参数方程;
(2)若直线
与
交于
,
两点,P为
上异于
,
的一点,求
面积的最大值.
![](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/96ab0107d12d056cede754a63375ab5a.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/925b34a1e7a48f450d883f9a0197e5c9.png)
(1)求
![](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/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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
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2022-03-21更新
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7卷引用:九师联盟(山西省)2022届高三3月质量检测数学(文)试题