名校
解题方法
1 . 假设视网膜为一个平面,光在空气中不折射,眼球的成像原理为小孔成像. 思考如下成像原理: 如图,地面内有圆
,其圆心在线段
上,且与线段
交于不与
重合的点
,
地面,且
,
点为人眼所在处,视网膜平面与直线
垂直. 过
点作平面
平行于视网膜平面. 科学家已经证明,这种情况下圆
上任意一点到
点的直线与平面
交点的轨迹(令为曲线
)为椭圆或圆,且由于小孔成像,曲线
与圆
在视网膜平面上的影像是相似的,则当视网膜平面上的圆
的影像为圆时,圆
的半径
为____________ . 当圆
的半径
满足
时,视网膜平面上的圆
的影像的离心率的取值范围为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
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2024-05-09更新
|
99次组卷
|
2卷引用:广东省广州市广东实验中学2024届高三教学情况测试(一)数学B卷
名校
2 . 如图曲线AB是以O为对称中心的椭圆的四分之一,A,B分别为长、短轴端点; 现只用圆规确定该椭圆的右焦点位置,步骤:以____ 为圆心以______ 为半径画弧与x轴的交点.(填序号即可)①点O;② 点A;③点B;④ OB长;⑤ OA长.
您最近一年使用:0次
3 . 曲线
上动点
与
构成
,若
,则实数
的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b67d93773ed34cfe79fd47025c9dac1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51296b06e4f0ac74bea949ce2d9faa6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ed4c4e8edbd179f3fc38a6653f18c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03ac378e1dd219184c4a0d722acb10f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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2024-02-23更新
|
973次组卷
|
2卷引用:广东2024届高三数学新改革适应性训练三(九省联考题型)
4 . 将1,2,3,…,9这9个数填入如图所示的格子中(要求每个数都要填入,每个格子中只能填一个数),记第1行中最大的数为
,第2行中最大的数为
,第3行中最大的数为
,则
的填法共有_______ 种.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b73abfe4bc26b1ded680d7abb1a2cac.png)
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2024-02-23更新
|
1662次组卷
|
7卷引用:广东省江门市第一中学2023-2024学年高二下学期第一次段考数学试题
广东省江门市第一中学2023-2024学年高二下学期第一次段考数学试题广东省深圳市福田区红岭中学2023-2024学年高二下学期期中考试数学试卷河北省部分重点高中2023-2024学年高三上学期2月期末考试数学试题河南省部分名校2024届高三上学期期末检测数学试题江苏省盐城市滨海县五汛中学2023-2024学年高三下学期高考适应性考试数学试题(已下线)第六章计数原理总结 第二练 数学思想训练(已下线)计数原理与二项式定理-综合测试卷B卷
名校
5 . 椭圆
:
的左焦点为
,右焦点为
,
在
上,
轴上一点
使
恒成立,则
,
的取值分别是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c82e7d9f4f7ace849e09e9adcb786b7f.png)
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名校
解题方法
6 . 设集合
为满足
,
,
的空间向量
,
,
中可能出现的两两共线的向量组数组成的数集,集合
,若
,则
的取值范围为______ ,当
最小时,
的取值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44ee0b48b17112965d224bd169314f5c.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2024-02-21更新
|
535次组卷
|
2卷引用:广东省广州市华南师范大学附属中学2024届高三上学期数学周测试题(12)
名校
解题方法
7 . 函数
的导函数为
,若在
的定义域内存在一个区间
在区间
上单调递增,
在区间
上单调递减,则称区间
为函数
的一个“渐缓增区间”.若对于函数
,区间
是其一个渐缓增区间,那么实数
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d06aee1856f9f2023dacd2ebe8fa8291.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2024-02-20更新
|
473次组卷
|
2卷引用:广东省(深圳外国语、东莞东华高级中学、阳江一中、河源中学)2023-2024学年高二下学期阶段性考试数学试题
解题方法
8 . 《测圆海镜》是金元时期李治所著中国古代数学著作,是中国古代论述容圆的一部专著,如第2卷第8题的“弦外容圆”问题是一个勾股形(直角三角形)外与弦相切的旁切圆问题,已知在
中
,
,
,点
在第一象限,直线
的方程为
,圆
与
延长线、
延长线及线段
都相切,则圆
的标准方程为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40630a669f4eedf626bc24851df10c85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852b303689c31189cd47bb4a3220f9fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/091c83390d0755e1b72755cf37490351.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dea2ae9d515f9ab351ad72306b776ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
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2024-02-14更新
|
126次组卷
|
2卷引用:广东省河源市2023-2024学年高二上学期期末考试数学试题
解题方法
9 . 2023年11月5至10日,中国国际进口博览会在上海举办,被誉为“黄皮火龙果”的厄瓜多尔麒麟果(图1)首次来到进博展台,其轴截面轮廓可近似看成椭圆(图2),A,C,B,D为椭圆的四个顶点,且
,则该椭圆的离心率为_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f3343c04f39d62be107ee552132d15.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/14/9c0135e6-c7bb-491c-aa06-75ef1f684124.png?resizew=280)
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解题方法
10 . 佛山是全国著名的工业城市,这里生产的部分产品通过水路运输到全国乃至全世界.下图1是佛山一个货运码头的吊机,其作用是完成集装箱的装船或卸船.为了研究其结构的稳固性,工程师把一个吊机的部分结构(图1中圈住部分)画成图2的空间几何体
.若四边形
是矩形,
,
,
,
,
,
,则直线
与
所成角的余弦值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b92a72e2b717ef70ea4d5c64f8173a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac7c3bffbe68a0b70f084d7be59c4029.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f121646549116bba24e250f3bec6dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4901a7eda97d6a307db76c4fb196ba3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/14/990ee89d-5319-47f4-81c3-c83b2e32082b.png?resizew=319)
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