名校
解题方法
1 . 已知
、
是椭圆
的两个焦点,以线段
为边作正三角形
,若边
的中点在椭圆上,则椭圆的离心率是( )
![](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/643ef7d761de0e794fc39937dc72ac6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7a6919a10602b63c55a9bb6fee29c85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b67528f875a6d4bac8bbf784f7b66a0.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2023-07-21更新
|
1069次组卷
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5卷引用:浙江省七彩阳光联盟2022-2023学年高二上学期期中数学试题
浙江省七彩阳光联盟2022-2023学年高二上学期期中数学试题福建省厦门第二中学2022-2023学年高二上学期第二次阶段考(12月)数学试题(已下线)3.1.2 椭圆的简单几何性质(精讲)-2023-2024学年高二数学《一隅三反》系列(人教A版2019选择性必修第一册)(已下线)专题02 期中真题精选(压轴93题10类考点专练)(3)浙江省宁波市鄞州中学2023-2024学年高二上学期12月月考数学试题
2 . 已知椭圆
的左、右焦点分别为
,离心率为
,过点
的直线l交椭圆于A,B两点,若
的周长为8,则C的方程为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf56a7eb7cf44143f7275ad8f61be1b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/167863df11667e8bbdd204413d3b5137.png)
A. ![]() | B. ![]() | C. ![]() | D. ![]() |
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2023-02-25更新
|
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5卷引用:福建省福州市八县(市)2022-2023学年高二上学期期末联考数学试题
福建省福州市八县(市)2022-2023学年高二上学期期末联考数学试题福建省福州市八县(市、区)一中2022-2023学年高二上学期期末联考数学试题(已下线)专题20 椭圆-1河南省许昌市鄢陵县职业教育中心(升学班)2022-2023学年高二下学期期末考试数学试题(已下线)专题3.2 椭圆的简单几何性质【八大题型】-2023-2024学年高二数学举一反三系列(人教A版2019选择性必修第一册)
解题方法
3 . 已知椭圆
的左、右焦点分别为
,、
,点
是椭圆
短轴的一个顶点.若
是周长为6的等边三角形.
(1)求椭圆
的方程;
(2)作斜率为
的直线
,与椭圆交于A,B两点,点
为
的中点.若
、
的斜率分别为
、
,证明:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)作斜率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3389f53711264b0acba3ba6019f8b908.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c30a7506331e47342fb1e7d2e12d041.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a16c755ab3fea6ca99b13193a5d7e485.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/4efbccf49b1891b1f59159ed8ba243ff.png)
您最近一年使用:0次
解题方法
4 . 已知椭圆
的左、右焦点分别为
是椭圆
的左、右顶点,直线
过点
交椭圆
于
两点,若
是周长为
的等边三角形.
(1)求椭圆
的方程;
(2)设直线
分别交
轴于
两点,记
的面积分别为
,当直线
绕点
旋转(不与
轴重合)时,证明:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a31bac720f397377e57d19a48ada34c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967f7f19733332525f69445768c4db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](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/20ebaa32f4f1f4f807ca9aeb7fb29951.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3c07ebcbfacda073208d483c58e8a84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41322821ce31416fdac8dd6e0aa41c71.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/854be43a71207548612f94b0b4f8f5ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86e203b7c9a6600e0272c58a23733490.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a1b2f6fe4389b8ed64562af12c721ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/378f9e4b145cd2ce1a5d0a6b9cb4ea94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235f0a6fb218d28383e6f27f2df1f50f.png)
您最近一年使用:0次
解题方法
5 . 已知
是椭圆
上一点,
为椭圆的两个焦点,则
的周长为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cae00bdc6f8b564b6b15b32572c848b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
A.4 | B.5 | C.6 | D.8 |
您最近一年使用:0次
2023-02-23更新
|
342次组卷
|
2卷引用:四川省乐山市2022-2023学年高二上学期期末数学理科试题
解题方法
6 . 已知椭圆
:
的焦点分别为
,
,
为
上的动点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d5311c1fe01f603413874c047af8c06.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
您最近一年使用:0次
解题方法
7 . 一般地,我们把离心率为
的椭圆称为“黄金椭圆”,则下列命题正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/029d393bb07b7140905b85f550519de4.png)
A.若![]() ![]() ![]() ![]() ![]() |
B.若![]() ![]() |
C.若“黄金椭圆”的左焦点是![]() ![]() ![]() |
D.设过原点的直线与焦点在![]() ![]() ![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
8 . 已知F,
分别为椭圆
的左、右焦点,A,B是椭圆C上关于原点对称的两点,且已知A,B不是椭圆的顶点,过点A作
轴,垂足为E,直线BE与椭圆C的另一个交点为P,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8e55590555905eb4f57889bbd16e39a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69daca955a565fa537347dd0d93783f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8178c63d125ee6235feeb2fc70d02745.png)
A.四边形![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() |
您最近一年使用:0次
解题方法
9 . 已知椭圆C:
的左、右焦点分别为
,
,P是C上任意一点(异于左右顶点),O为坐标原点,M,N分别为线段
,
的中点,若四边形PMON的周长为6,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36f54caf7dd87fbb2866908f6baaf88a.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/9ac86e1c253297a377e14fb9a1689be8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0739793f234f8e86adc6177801ae7295.png)
A.C的长轴长为3 | B.C的离心率为![]() |
C.![]() | D.![]() |
您最近一年使用:0次
10 . 已知椭圆
内一点
,上、下焦点分别为
,
,直线
与椭圆
交于
,
两点,且
为线段
的中点,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97626607323a7c28900ecf4da111b08b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cd9ba40c267e83bd99a4763ede55bb1.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
A.椭圆的焦点坐标为![]() ![]() | B.椭圆![]() ![]() |
C.直线![]() ![]() | D.![]() ![]() |
您最近一年使用:0次
2023-02-09更新
|
493次组卷
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2卷引用:湖北省部分市州2022-2023学年高二上学期元月联考数学试题