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1 . 某中学开展劳动实习,学生加工制作零件,零件的截面如图(单位:
)所示,四边形
为矩形,
均与圆
相切,
为切点,零件的截面
段为圆
的一段弧,已知
,则该零件的截面的周长为( )cm(结果保留
)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/21/4a1d3064-c143-48cb-8fdc-0bab9229d564.png?resizew=192)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efa9fbcfb9595e2f031aa691db4564b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89e9785a8ffb637c91757fe01d3c23a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be926405fee81c68b02c826385eaae79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e453b6640e3dc4c7b7b2a996a2199ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eb908b33d2619706de2dd9b6ccd64f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/21/4a1d3064-c143-48cb-8fdc-0bab9229d564.png?resizew=192)
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-03-19更新
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3卷引用:河南省南阳市2022-2023学年高三第二次大练习数学(理)试题
2 . 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
的极坐标方程和直线
的直角坐标方程;
(2)若直线
与
轴交于点A,点
在曲线
上运动,求直线
斜率的最大值.
![](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/c1ba8088a73e9ea350567af28056598f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.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/a0701f379af5e1ba5761ebfc4a94a809.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
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2023-03-10更新
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2卷引用:湘豫名校联考2023届高三第一次模拟考试数学(文科)试题
3 . 在直角坐标系
中,曲线
,
的参数方程分别为为
(t为参数),
(
为参数).
(1)将
,
的参数方程化为普通方程;
(2)以坐标原点为极点,x轴正半轴为极轴建立极坐标系,直线l的极坐标方程为
,若直线l与
,
共有三个交点,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/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1624a2e861f8c6751ff4a7d144b38534.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0356c7d07362ee2e1887ae7f179b8423.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(1)将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)以坐标原点为极点,x轴正半轴为极轴建立极坐标系,直线l的极坐标方程为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6674dee2888356225b116559ee511d7.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/e170f206fdbbd834aad7580c727e2cc6.png)
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3卷引用:河南省top20名校联盟2023届高三下学期2月联考理科数学试题
2023·新疆·模拟预测
4 . 在直角坐标系xOy中,曲线C的参数方程为
(t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,直线l的极坐标方程为
.
(1)写出直线l的直角坐标方程;
(2)设曲线C与x轴的交点为A,B(点A在点B的左侧),若直线l上存在点M,满足
,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f0484f85454a1f4969b534d06f72857.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eff8cba80a5e8c641020c74444ece3c.png)
(1)写出直线l的直角坐标方程;
(2)设曲线C与x轴的交点为A,B(点A在点B的左侧),若直线l上存在点M,满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff3c8d44803d79c249ebc1f791e337bf.png)
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5 . 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,曲线
的极坐标方程为
.
(1)写出
的普通方程;
(2)若曲线
与
有两个交点
,则当
为何值时,
最大?并求出
的最大值.
![](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/407fcd22da9be13e83a2288a8e8323cc.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/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f18bf711ad049b7b75367c92e0d11f5d.png)
(1)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)若曲线
![](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/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/084cf5ffced059f5653ee2a1023518b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/084cf5ffced059f5653ee2a1023518b7.png)
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2卷引用:河南省部分名校2022-2023学年高三下学期学业质量联合检测文科数学试题
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解题方法
6 . 已知直线
与圆
相切,若函数
,满足
,对于任意的
恒成立,则实数
的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/044238be0ba36eba4b154b499ace202e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2865a1ac9fb5b9e80a29238b0fe208e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44f5e2d3c823bdfb969ebae2b559e8a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0994527aeb5c0a2e58d140e25fcad393.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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7 . 已知点C(2,0),直线kx-y+k=0(k≠0)与圆
交于A,B两点,则“△ABC为等边三角形”是“k=1”的( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e406e4c2be675e0161514c611e9f4b27.png)
A.充要条件 | B.充分不必要条件 |
C.必要不充分条件 | D.既不充分也不必要条件 |
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22-23高三上·河南·期末
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8 . 已知圆
上的点
均满足
则
的最大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/946ae5de1914637f2f76e98bcf2bbdad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf0d139c9810361b4971904a943856b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af3d5f42c4d2913082350d5e88aa3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-01-15更新
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173次组卷
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3卷引用:河南省名校联盟2022-2023学年高三上学期1月新未来联考理科数学试题
(已下线)河南省名校联盟2022-2023学年高三上学期1月新未来联考理科数学试题河南省信阳高级中学2022-2023学年高三上学期期末考试理科数学试题江西省九所重点中学2023届高三第二次联考联合考试数学(理)试题
22-23高三上·河南·期末
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解题方法
9 . 在平面直角坐标系
中,已知圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5bbb709522dba9425a6b45ee671298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33ac53abed7d45b6fff5c9313969851a.png)
被
轴截得的弦长为2,且与直线
相切,则实数
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5bbb709522dba9425a6b45ee671298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33ac53abed7d45b6fff5c9313969851a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bf8197e4f3fd18815045d29c357a863.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08b9f0b9e53a83e68f5fec944f343119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() | C.3 | D.![]() |
您最近一年使用:0次
2023-01-15更新
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260次组卷
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3卷引用:河南省名校联盟2022-2023学年高三上学期1月新未来联考文科数学试题
(已下线)河南省名校联盟2022-2023学年高三上学期1月新未来联考文科数学试题河南省信阳高级中学2022-2023学年高三上学期期末考试文科数学试题陕西省子长市中学2024届高三上学期第三次模拟考试理科数学试题
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10 . 已知圆
与过原点
的直线
相交于A,B两点,点
为x轴上一点,记直线
的斜率分别为
,
,若
,则实数
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd64383e516a7d2d989daf6d09034ab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ca8b6ac96dfe0046b7ca1745176ca22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84bfec4efcc9f0e656d6864daaaef55d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790ef3382b1c731f2885eecfd92c2a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83d200a411fbc2f50ad72f1fd729a7d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
A.![]() | B.![]() | C.2 | D.3 |
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