1 . 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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解题方法
2 . 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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名校
3 . “方程
表示椭圆”是“
”的( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eb6a157e6802d54f117f7eaec2b030d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7f7ba96ba2b49b1c43c53f0379b6388.png)
A.充分不必要条件 | B.必要不充分条件 |
C.充要条件 | D.既不充分也不必要条件 |
您最近一年使用:0次
2024-02-05更新
|
715次组卷
|
5卷引用:2.2.1 椭圆的标准方程(十三大题型)(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)
(已下线)2.2.1 椭圆的标准方程(十三大题型)(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)贵州省毕节市七星关区第一教育集团(毕节二中)2023-2024学年高二上学期期末考试数学试卷湖北省恩施州利川市第一中学2023-2024学年高二下学期开学考试数学试题湖北省荆州开发区高级中学2023-2024学年高二下学期3月月考数学试题安徽省六安市田家炳实验中学2023-2024学年高二下学期开学测试数学试题
名校
解题方法
4 . 已知曲线
与y轴交于A,B两点,P是曲线C上异于A,B的点,若直线AP,BP斜率之积等于
,则C的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c623fe58727acdd1fd4964b4947df4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03aa30b6d5bfcefb197cc2046479ed65.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-02-05更新
|
440次组卷
|
3卷引用: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)
(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)湖北省荆州市八县市区2023-2024学年高二上学期1月期末联合考试数学试题河南省南阳市第一中学校2023-2024学年高二下学期开学考试数学试题
解题方法
5 . 已知
为椭圆
的两个焦点,过
的直线与C交于M,N两点.若
,
,则C的离心率为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25b7b8327139b0058a512a8b256f1a3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e7155f4135d1d728947cb3986675533.png)
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名校
6 . 已知椭圆
的左右焦点分别为
,
,点B为短轴的一个端点,则
的周长为___ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b747db7eaf469c6d1607e4b0d028299f.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/47444b5fbc4252516d54263062e47c81.png)
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7 . 已知△ABC的两个顶点坐标分别是
和
,边AB,AC所在直线的斜率的乘积是
,则顶点A的轨迹方程为_____
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23b9fc6ffcd8047efb5e7748fb7e4ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df957b06efbd4bb374bf2aa248ca43c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b889efe020137b112bfafaa8e0becda4.png)
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2024高二上·全国·专题练习
解题方法
8 . 分别写出满足下列条件的椭圆的标准方程:
(1)焦距为4,且经过点
;
(2)求经过点
和点
的椭圆方程.
(1)焦距为4,且经过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dba0ddcdf6ed46447b5d4885674700a9.png)
(2)求经过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bddd5d20576fb15ced9e028d965e708.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ac101eab8342edcef93ae13226dbf45.png)
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2024高二上·全国·专题练习
9 . 已知
,
分别是椭圆
的左、右焦点,点
在椭圆上,
是坐标原点,且
,则
的面积等于________ .
![](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/c06ffc3051183ecdd0fa98799095bc13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a142a46b1c34c0f6a1bfeddaac58b9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/002ed1ebb2cb936e10ab478789f91c7c.png)
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2024高二上·全国·专题练习
10 . 已知定点
,点
为椭圆
的右焦点,点M在椭圆上移动,求
的最大值与最小值的和为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afc83347d419c0aae5b61c14f4164bdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e78f1a9cc4dedc05c175ab99b288b9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e701a3eba9d5fe7001ed4ddf5867e921.png)
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