名校
解题方法
1 . 已知椭圆
:
的左、右焦点分别为
、
,又
,
,且直线
,
的斜率之积为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/347b68f42934c74e0d759a67613a1da9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/104c7ac4a841a2a7bd3e39d2b3fb03ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3421f0c0345cf17ede6ca5ce4c50bde2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4b9486ec9dca95979803bf91ca6c337.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fa6e5a12543f954be1a6057c6b2ed51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbad65b3d744b70da2480eee1cdb587.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29418e5014731850c55565b6bf47aa41.png)
A.![]() |
B.![]() |
C.![]() ![]() |
D.若![]() ![]() ![]() ![]() |
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名校
解题方法
2 . 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)
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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
解题方法
3 . 已知椭圆
的离心率为
其左右焦点分别为
下顶点为A,右顶点为B,
的面积为 ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acac46663213391d6b2615cecda7e48c.png)
(1)求椭圆 C 的方程;
(2)设不过原点O 的直线交C于M、N两点,且直线
的斜率依次成等比数列,求
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a869ea8dd6c0388b88436a856ebad3a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ba447f2abb9bd37cc8d3f607f7e694a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1689df51a5cf26cec30ad609ddfefb9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3c07ebcbfacda073208d483c58e8a84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acac46663213391d6b2615cecda7e48c.png)
(1)求椭圆 C 的方程;
(2)设不过原点O 的直线交C于M、N两点,且直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d81e42001b5d929e325fa0c801b7242c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4f02028a3847c4807c2d3cf0ea7efb8.png)
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2024-04-24更新
|
397次组卷
|
3卷引用:四川省德阳市2024届高三下学期“三诊”考试(理科)数学试题
名校
4 . 已知椭圆
的左,右焦点分别为
,将
上所有点的横坐标与纵坐标分别伸长到原来的
倍得到椭圆
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/130b07a72336579fe52980da6dd7dd74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e70f280d062923a39c0c881aad5d429.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b991d4173297923de7c4c1fa48bfae61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3113c748ec660388c3ae764f40a309f.png)
A.若![]() ![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() |
您最近一年使用:0次
2024-04-12更新
|
363次组卷
|
2卷引用:河南省TOP二十名校2024届高三下学期4月冲刺一数学试卷
解题方法
5 . 已知椭圆
,
,则
的离心率为______ .(写出一个符合题目要求的即可)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25ebccfc1862bce7f44daef18bcc34e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/573394d925f221e828978ba5b528dd39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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解题方法
6 . 已知椭圆
的离心率为
,且点
在椭圆上.
的标准方程;
(2)如图,若一条斜率不为0的直线过点
与椭圆交于
两点,椭圆
的左、右顶点分别为
,直线
的斜率为
,直线
的斜率为
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd0e6f5ff0f4fa113f4cad9f72fbbcc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)如图,若一条斜率不为0的直线过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc6554ac3dff4a59833e407db887f6e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.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/7785afeeaf274892253d04b4f693b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07765d282ff61d422aba3fc5f0b61e2a.png)
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2024-02-01更新
|
2724次组卷
|
7卷引用:湖南省长沙市雅礼中学2024届高三一模数学试卷
湖南省长沙市雅礼中学2024届高三一模数学试卷云南省三校2024届高三高考备考实用性联考卷(五)数学试题(已下线)2.2.2 椭圆的性质(十八大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)云南省玉溪市第一中学2023-2024学年高二下学期3月月考数学试题(已下线)专题07 直线与圆、圆锥曲线江西省宜春市丰城市第九中学2023-2024学年高二下学期开学考试数学试题安徽省阜阳第一中学2023-2024学年高二下学期4月月考数学试题
2024高三·全国·专题练习
名校
解题方法
7 . 已知
为坐标原点,
为椭圆
的左、右焦点,
是椭圆上异于顶点的一点,点
是以
为底的等腰三角形
的内切圆圆心,过
作
,垂足为
,则椭圆的离心率为______ .设内切圆与
轴相切于点
,则
的面积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20537b56f64f6b7a808402981257c96d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0739793f234f8e86adc6177801ae7295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf8a7029669bf1774a24f3ef6273ca88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8c3e0f50ddb6819979cf96cce25248e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57da117f4143ccf0d6d8b26829197813.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e30467196dfcb2cc2f388fb9b2ab15e8.png)
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解题方法
8 . 已知椭圆和双曲线有相同的焦点
,它们的离心率分别为
,点
为它们的一个交点,且
.当
取最小值时,
的值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f994a876391534efe497dc115a53e3fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d432bcd7c9767b85bd4f95e7e81f7a9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df65dbf36949aecc9a6997716c76290f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/582c6bd5d7bd4d9aed58c1ca0b4264a6.png)
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2024高三·全国·专题练习
名校
解题方法
9 . 若椭圆
的焦点在y轴上,过点
作圆
的切线,切点分别为A、B,直线AB恰好和椭圆只有一个交点,则椭圆内接矩形最大时的离心率是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a8cf5b30bde0f2414c21e4f04bf9a44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bac7c28099bfbb7dc2a45ad166eace05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
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解题方法
10 . 已知农历每月的第
天(
,
)的月相外边缘近似为椭圆的一半,方程为
,其中
为常数.根据以上信息,下列说法中正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0a75c002da59c2ec5ef683ba618d973.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c569e0afed481a3333cab3dea70f1222.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01010b76f1344143f401238db4043dea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/803c45a61d25e49e0db689f959cfb93f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
A.农历每月第![]() ![]() ![]() ![]() |
B.月相外边缘上的点到椭圆焦点的距离的最大值为![]() |
C.月相外边缘的离心率与![]() |
D.农历初六至初八的月相外边缘离心率在区间![]() |
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