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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/137d33c8575602cb3480ba3825dece9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a7442b64b37f685bc3ae88ff450c1a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70e92e4810c9461c39fae1acde95e489.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.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/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3dc6893e52bbca0d011ac46845334d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
您最近一年使用:0次
2024-05-09更新
|
99次组卷
|
2卷引用:四川省成都市实验外国语学校2023-2024学年高二上学期期末能力测评数学试题
名校
解题方法
2 . 某中学开展“劳动创造美好生活”的劳动主题教育活动,展示劳动实践成果并进行评比,某学生设计的一款如图所示的“心形”工艺品获得了“十佳创意奖”,该“心形”由上、下两部分组成,并用矩形框
虚线
进行镶嵌,上部分是两个半径都为
的半圆,
分别为其直径,且
,下部分是一个“半椭圆”,并把椭圆的离心率叫做“心形”的离心率.
,则当该矩形框面积最大时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/258e40e3883271c3580c1d3c805dcac6.png)
__________ ;
(2)若
,图中阴影区域的面积为
,则该“心形”的离心率为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd995178601c2ad7b40f973d268c7bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d578394cd8e4d7a705599269c512960.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ce072bcd423b56c827e40f0b731de85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8da45c443af7994a26ffa9d8894e7262.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/258e40e3883271c3580c1d3c805dcac6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7551011cfb75b26f35b07d6617c6a18b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df9eb8f0efaf6fe8a69150fcdf3c83fc.png)
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2024-03-03更新
|
280次组卷
|
3卷引用:北京市第二中学2023-2024学年高二上学期12月第二学段考试数学试卷
名校
解题方法
3 . 如图所示圆锥,
为母线
的中点,点
为底面圆心,
为底面圆的直径,且
,
,
的长度成等比数列,一个平面过
,
,与圆锥面相交的曲线为椭圆,若该椭圆的短轴与圆锥底面平行,则该椭圆的离心率为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d4db9b82b67efe45a02fca32bfcf5dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c2bc5e50b8dfa02601c70822252854a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d4db9b82b67efe45a02fca32bfcf5dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/11/164b88dd-e192-4fb5-9554-844056056749.png?resizew=180)
您最近一年使用:0次
2023-03-10更新
|
1459次组卷
|
3卷引用:江西省抚州市七校2022-2023学年高二下学期期中联考数学试题
名校
解题方法
4 . 在生活中,可以利用如下图工具绘制椭圆,按照这个原理,已知O是滑杆上的一个定点,D可以在滑杆上自由移动,线段
,点B,E是AD上两点,E是AD中点,且
,如图,过B作AD的垂线,满足
,则点E所形成的轨迹
的离心率![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1b988dbce5a9198d61842c95e7747d9.png)
________ ;点C所形成的轨迹
的离心率![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71ced3c956c7292540692adf70b41fd4.png)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43bce604c2a5730b5d9d8bd642f4484d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17ad7e0e730caaebab54e28873c38543.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce5256233ba43fccd2732b983d533f08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1b988dbce5a9198d61842c95e7747d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71ced3c956c7292540692adf70b41fd4.png)
![](https://img.xkw.com/dksih/QBM/2022/5/19/2982704523100160/2984378751426560/STEM/9d582248-3990-417c-bcee-918d6e2003fe.png?resizew=518)
您最近一年使用:0次
名校
解题方法
5 . 如图①,用一个平面去截圆锥,得到的截口曲线是椭圆.许多人从纯几何的角度出发对这个问题进行过研究,其中比利时数学家Germinal dandelin(1794-1847)的方法非常巧妙,极具创造性.在圆锥内放两个大小不同的球,使得它们分别与圆锥的侧面,截面相切,两个球分别与截面相切于E,F,在截口曲线上任取一点A,过A作圆锥的母线,分别与两个球相切于C,B,由球和圆的几何性质,可以知道,AE=AC,AF=AB,于是AE+AF=AB+AC=BC.由B,C的产生方法可知,它们之间的距离BC是定值,由椭圆定义可知,截口曲线是以E,F为焦点的椭圆.
如图②,一个半径为2的球放在桌面上,桌面上方有一个点光源P,则球在桌面上的投影是椭圆.已知
是椭圆的长轴,
垂直于桌面且与球相切,
,则椭圆的离心率为__________ .
![](https://img.xkw.com/dksih/QBM/2021/5/8/2716860912132096/2717542584033280/STEM/a1759ca8-768f-4e32-a6ff-630c3079b0fe.png?resizew=212)
如图②,一个半径为2的球放在桌面上,桌面上方有一个点光源P,则球在桌面上的投影是椭圆.已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/473913c0887bb64d386f4c02f1853452.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/800c5e266b4ad8462a46970f0a232d52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/435c1ddef3cc12a0aa2c3576245bf230.png)
![](https://img.xkw.com/dksih/QBM/2021/5/8/2716860912132096/2717542584033280/STEM/a1759ca8-768f-4e32-a6ff-630c3079b0fe.png?resizew=212)
![](https://img.xkw.com/dksih/QBM/2021/5/8/2716860912132096/2717542584033280/STEM/eb29d299-12a5-44cf-9626-c5d8bae758ca.png?resizew=336)
您最近一年使用:0次
2021-05-09更新
|
2389次组卷
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7卷引用:3.1 椭圆(难点)(课堂培优)-2021-2022学年高二数学课后培优练(苏教版2019选择性必修第一册)
(已下线)3.1 椭圆(难点)(课堂培优)-2021-2022学年高二数学课后培优练(苏教版2019选择性必修第一册)东北师大附中2021届高三第四次模拟考试数学(理)试题东北师大附中2021届高三第四次模拟考试数学(文)试题山西省运城市2022届高三上学期入学摸底测试数学(文)试题河南省名校联盟2021-2022学年高三下学期第一次模拟理科数学试题(已下线)专题8-2 立体几何截面问题的十种题型-2022年高考数学毕业班二轮热点题型归纳与变式演练(全国通用)(已下线)专题7-2求曲线方程和动点轨迹归类-2