1 . 已知
,
分别为椭圆E:
的左右焦点,其离心率
,O为坐标原点,过O作直线l交椭圆于A,B两点,
的面积最大值为
.
(1)求椭圆E的方程;
(2)若过点
的直线
交椭圆E于C,D两个不同的点,且
.求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6adbefade88c1539fc8d722725bf57ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3c07ebcbfacda073208d483c58e8a84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
(1)求椭圆E的方程;
(2)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2348e3eb68118c6f7c6132c546525ba0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b7bac25e1444ef26341d98b0218e82c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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2 . 已知椭圆
:
的左、右焦点为
,
,点
,
,
为椭圆
上一动点,过点
的直线
交椭圆于
,
两点,则下列说法正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb4717d7fa6d522090c5e949f650bd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f5e0005baadf4e655c1b377487c8af8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/138bcbc42bc1c7230c4a325aee56153b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd1badfc214fee86f3e31cbf5cd35090.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
A.若![]() ![]() ![]() |
B.![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() ![]() |
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解题方法
3 . 已知椭圆
的离心率为
,短轴长为
.
(1)求椭圆C的标准方程;
(2)设椭圆C的左、右焦点分别为
,直线
与椭圆C相切,点
到直线l的距离分别为
,求
的最小值.
![](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/38387ba1cadfd3dfc4dea4ca9f613cea.png)
(1)求椭圆C的标准方程;
(2)设椭圆C的左、右焦点分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c287201dc8f4b7e1a8dd41920654656.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf2f1c1409a06278e847e6b573cef254.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2a4b32d388558eb9a9e4f0f2dd57c09.png)
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解题方法
4 . 已知椭圆
的离心率为
,左顶点为
,直线
与椭圆
交于
,
两点.
(1)求椭圆的
的标准方程;
(2)若直线
,
的斜率分别为
,
,且
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/913f78382630e50543e5f7192cae3ed3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(1)求椭圆的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d454c82d9e52747563d47b68099249.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/e28f58710dc1ffdc9a3da0db28269133.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d44e8bc37ed03f44470762748a8f942a.png)
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解题方法
5 . 已知直线
和椭圆
若对任意实数
,直线
与椭圆
恒有公共点,且存在实数
使得直线
与椭圆
仅有一个公共点,
的离心率的取值范围为
,则椭圆
的长轴长的取值范围是
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ede334d7b062fd6014c473b5f7d5adfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2607fad0ba617be3e88d2d1d77142ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/9c995153374d72ec7bb778cd420fb98c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://img.xkw.com/dksih/QBM/2022/12/6/3124841894461440/3125297948983296/STEM/c233872f614846eb98c76d039b191c71.png?resizew=4)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
6 . 国家体育场“鸟巢”的钢结构鸟瞰图如图1所示,内外两圈的钢骨架是离心率相同的椭圆;某校体育馆的钢结构与“鸟巢”相同,其平面图如图2所示,若由外层椭圆长轴一端点A和短轴一端点B分别向内层椭圆引切线AC,BD,且两切线斜率之积等于
,则椭圆的离心率为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/6/b9fc3953-981d-45b7-b222-5aef6a61adc1.png?resizew=163)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/6/2c107155-53be-4c62-bfad-01f894e48a99.png?resizew=191)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f30d314a642667fef559032264647366.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/6/b9fc3953-981d-45b7-b222-5aef6a61adc1.png?resizew=163)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/6/2c107155-53be-4c62-bfad-01f894e48a99.png?resizew=191)
A.![]() | B.![]() | C.![]() | D.![]() |
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2022-12-06更新
|
1202次组卷
|
5卷引用:安徽省合肥市六校联盟2022-2023学年高二上学期期中联考数学试题
安徽省合肥市六校联盟2022-2023学年高二上学期期中联考数学试题浙江省杭州第四中学下沙校区2022-2023学年高二上学期期末数学试题广东省东莞市东莞外国语学校2023-2024学年高二上学期第二次段考数学试题(已下线)第八章 解析几何 专题8 有关椭圆的离心率问题 高中数学优质试题一题多解和变式训练新疆维吾尔自治区阿克苏地库车市第二中学2023-2024学年高二上学期期中数学试题
名校
解题方法
7 . 已知椭圆C:
(
)与x轴分别交于
、
点,N在椭圆上,直线
,
的斜率之积是
.
(1)求椭圆C的方程;
(2)求点N到直线l:
的最大距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/122cf7a2f27fadf126b282fb1b3e1533.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da50ebd2656745259525c8b157e389e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecf41a917940c6d8a30da627c7b3e79f.png)
(1)求椭圆C的方程;
(2)求点N到直线l:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc47b86b49e3d4416404f8f3d3ed0460.png)
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解题方法
8 . 已知曲线C的方程为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d9ff81017e5541e9357bd16089dbca.png)
(1)判断曲线C的形状;
(2)设直线
与曲线C交于不同的两点M,N,且
(O为坐标原点),求曲线C的方程.
(3)已知点
,
,若点P为(2)中所求曲线上一动点,且满足
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d9ff81017e5541e9357bd16089dbca.png)
(1)判断曲线C的形状;
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb41fc6a64ac7f649b3ea3e969738dda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab760f42892e987055c09495bd014554.png)
(3)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4504b40c31bed273f8c0ce9ec96e6cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5897078ac133453a5fe7eeb979487464.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d462ecbfd4c6937d4a58725b809df966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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解题方法
9 . 如图,已知圆
的方程为
,圆
的方程为
,若动圆
与圆
内切与圆
外切.
![](https://img.xkw.com/dksih/QBM/2022/11/13/3108966101344256/3109649285259264/STEM/83b5ed3f27734255a12326f5a9c4b48b.png?resizew=186)
(1)求动圆圆心
的轨迹
的方程;
(2)过点
作互相垂直的两条直线分别交
于点
和
,求四边形
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1bb25ddbace840c056d1c284bea0c77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a083a009c6e14e9ec7d38cbb1f61928b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://img.xkw.com/dksih/QBM/2022/11/13/3108966101344256/3109649285259264/STEM/83b5ed3f27734255a12326f5a9c4b48b.png?resizew=186)
(1)求动圆圆心
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c593ebdb2f1934a0cb56f8c44f454f8.png)
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解题方法
10 . 已知椭圆
:
的左、右顶点分别为A,B,左焦点为F,
,
.
(1)求椭圆
的标准方程;
(2)设点P为x轴上的点,经过F且不垂直于坐标轴的直线l与C交于M,N两点,且
.证明;
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd299e799aab9f5ef02b48979d667c15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d4ff16868e1351b444692a4b010ccd9.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设点P为x轴上的点,经过F且不垂直于坐标轴的直线l与C交于M,N两点,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5929048ce5167abc4750589f2e21841.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c4f9e16b81beb36d0a6fdb2edda51a6.png)
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