2023高三·全国·专题练习
解题方法
1 .
为等边
内一动点,且
,则
的最小值为__ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b257f5c49551e508b5483b2a695b31ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b220012a4cb588bef9477333abc4d5a.png)
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解题方法
2 . 数学中有许多形状优美的曲线,如星形线,让一个半径为
的小圆在一个半径为
的大圆内部,小圆沿着大圆的圆周滚动,小圆的圆周上任一点形成的轨迹即为星形线.如图,已知
,起始位置时大圆与小圆的交点为
(
点为
轴正半轴上的点),滚动过程中
点形成的轨迹记为星形线
.有如下结论:
上任意两点间距离的最大值为
;
② 曲线
的周长大于曲线
的周长;
③ 曲线
与圆
有且仅有
个公共点.
其中正确的序号为________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f953d79ae365a13161ad83f022362f5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7551011cfb75b26f35b07d6617c6a18b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3304e23f3b0f9569c4140ca89b6498.png)
② 曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f17960ae10e3ec8154f478631fa6a79b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
③ 曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f5d967ad135991b6075ee45df55643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
其中正确的序号为
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2022-01-15更新
|
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6卷引用:北京市石景山区2022届高三上学期期末数学试题
北京市石景山区2022届高三上学期期末数学试题北京市首都师范大学附属中学2022届高三下学期开学检测数学试题(已下线)重难点10四种解析几何数学思想-2北京市第二中学2022-2023学年高二上学期11月学段考试数学试题(已下线)单元高难问题02数学思想方法在解决与圆有关问题中的应用(各大名校30题专项训练)(原卷版)(已下线)专题1 直线与圆的位置关系【练】(压轴小题大全)
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3 . “曼哈顿距离”是十九世纪的赫尔曼•闵可夫斯基所创,定义如下:在直角坐标平面上任意两点
的“曼哈顿距离”为
,已知动点
在圆
上,定点
,则
两点的“曼哈顿距离”的最大值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e3a1467ecf286e3cadaf5aa006606f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c913b3abbf53d81fcf25bf83d4ae3756.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08227ca941898eb34941f446ca8b1de8.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
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3卷引用:江苏省盐城中学等四校联考2024届高三上学期12月阶段检测数学试题
4 . 在等腰直角三角形
中,
,
为斜边
的中点,以
为圆心,
为半径作
,点
在线段
上,点
在
上,则
的取值范围是 ________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
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解题方法
5 . 已知动点
满足
,若直线l过点
与点M的轨迹相切,则直线l的方程为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d259822ab64b8626f3893b8432673358.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9519dad0c81187bd62291462f5d9ac60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd243fab0af865af67a2ab817e909cf5.png)
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6 . 直线
被曲线
(
为参数)截得的弦长为
,则实数
的值为_______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/292fc234260672633fd445545a932553.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a89efbc9a30e9f3e9ee4201a6fb9030.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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7 . 已知实数
满足
,则
的最大值为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b3d38c6d230bfe3e2dfc187fa0f9341.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c20a63ca6307dc033abf581e7b38fe16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/450398974b1561ca801e102e16df6789.png)
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8 . 已知O为坐标原点,点
,P为圆
上一点,则
的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3793d98d60080b414ac8acbb975e048f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1189cef4edfd44fd9d7e48b22495072.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eea2a4cfbf9b8eea0e33a6393d3d587e.png)
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2卷引用:陕西省榆林市十校2024届高三上学期12月联考数学(文)试题
9 . 设
为平面上一定点,
为动点,则当
由0变化到
时,线段
扫过的面积是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/448c0a5ee776d19ce8e42ac9a5fd27c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf4cb23e5a9f069eaf73b1bf572532b6.png)
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10 .
是圆
上一动点,
为
的中点,
为坐标原点,则
的最大值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/096c252be3fddf7763db5761150d8eda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a01f70150a147c9b156ee39e8a08b2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
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