名校
1 . 已知曲线
,其中
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a6567908622a20195c8423d1a3682b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/211bb9d7aadd19ea6593f3bddcc6205b.png)
A.存在![]() |
B.存在![]() |
C.若C为椭圆,则![]() |
D.若C为双曲线,则![]() |
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解题方法
2 . 已知正方形
的四个顶点均在椭圆
上,
的两个焦点
分别是
的中点,则
的离心率是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab0fe9059acc47d2447576e1260c4622.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c4cd264c97c1f261229925cc5a6761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
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名校
3 . 已知椭圆
的左右焦点分别是
,
,过
的直线与
相交于A,B两点,若
,
,则
的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.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/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/595204f5b59b488a4532af8f0555c77a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d2962f9b7b3d3a2d9a4ceb99a19b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-03-22更新
|
553次组卷
|
2卷引用:福建省福州市八县(市)协作校2023-2024学年高二上学期期末数学试题
名校
解题方法
4 . 已知椭圆C:的左、右焦点分别为F1,F2,点P在椭圆C上,则( )
A.椭圆C的离心率为![]() | B.椭圆C的离心率为![]() |
C.![]() | D.![]() |
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2024-03-20更新
|
291次组卷
|
2卷引用:浙江省杭州四中2023-2024学年高二上学期期末数学试题
名校
解题方法
5 . 已知椭圆C:
的左、右焦点分别为
,
,P为C上一点,满足
,以C的短轴为直径作圆O,截直线
的弦长为
,则C的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.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/c2427943a38dcd93c9ec9b735ffc9fe5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac86e1c253297a377e14fb9a1689be8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7ec189df9aa2b3c46de719d0057a05f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-03-14更新
|
1062次组卷
|
5卷引用:海南省海口市2024届高三摸底考试数学试题
解题方法
6 . 一般地,我们把离心率相等的两个椭圆称为相似椭圆
已知椭圆
和椭圆
是相似椭圆,则下列结论中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/882a6e8f86e28c2382ab50e2c8ab0c0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dd22e9c3540f4e20a65368d5dab62e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf79ba6e74f87247a79d07ccab37dc39.png)
A.椭圆![]() ![]() |
B.![]() ![]() |
C.![]() ![]() |
D.双曲线![]() ![]() |
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解题方法
7 . 已知椭圆
的右焦点为
,
为坐标原点,
上位于第一象限的点
满足
,若直线
的斜率为
,则
的离心率为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24550b13dbecf7d86c7054250e987274.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d83eeb3772ef399193d5be5e72f58447.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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8 . 椭圆
:
的左右焦点分别为
,
,
为坐标原点,给出以下四个命题:
①过点
的直线与椭圆
交于
,
两点,则
的周长为12;
②椭圆
上存在点
,使得
;
③椭圆
的离心率为
;
④
为椭圆
:
上一点,
为圆
上一点,则点
,
的最大距离为4.
其中正确的序号有______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbf679418512d6ad973531df808fd267.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/1dde8112e8eb968fd042418dd632759e.png)
①过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.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/d3c07ebcbfacda073208d483c58e8a84.png)
②椭圆
![](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/2ce67f2138e7295cd72d66b2908cb6de.png)
③椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
④
![](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/fbf679418512d6ad973531df808fd267.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
其中正确的序号有
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名校
9 . 已知椭圆
的离心率为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc1500c00ba093a3834e691180e4d777.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
您最近一年使用:0次
2024-03-06更新
|
905次组卷
|
3卷引用:四川省成都市第七中学2023-2024学年高三上学期期末考试文科数学试卷
解题方法
10 . 如图1所示,套娃是一种木制玩具,一般由多个相同结构的空心木娃一个套一个组成,套娃的截面可近似看成由圆和椭圆的一部分组成.建立如图2所示的平面直角坐标系,圆A:
的圆心是椭圆的上顶点,半径是椭圆的短半轴长,则椭圆的离心率为______________ ;若动直线
与圆的上半部分和椭圆的下半部分分别交于B,C两点,则当
的面积最大时,
的值为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/385c0c2bd59b09791069d1952ae62904.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6f7b16d65f1b2b8bea8cf4a83fde925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72daa42d22bc47a9585772e5c56b0c54.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/4/88aca1ff-9b2e-4cc4-b150-5d61d290af18.png?resizew=326)
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