解题方法
1 . 已知椭圆
,点
、
分别为椭圆的左、右焦点.
(1)若椭圆上点
满足
,求
的值;
(2)点
为椭圆的右顶点,定点
在
轴上,若点
为椭圆上一动点,当
取得最小值时点
恰与点
重合,求实数
的取值范围;
(3)已知
为常数,过点
且法向量为
的直线
交椭圆于
、
两点,若椭圆
上存在点
满足
(
),求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/533b93dd6eb6b474481247736699c76c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
(1)若椭圆上点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2dfb22c6f1c155747100e7536cd1abd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4ef569668e797b1e94257fd5f4384dd.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b312367cf51225ea3bfbee2103b0c30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a670d12554358604dc27abf2eaf1732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af4c79c684c65c68dea50c101df7f28c.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb7d14d32f1624f5e65b44079cc96de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc019674727e52ae48ca67e184ca5e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1adebff9fb726cd58eda1ef994890901.png)
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2024-04-01更新
|
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3卷引用:上海市浦东新区2024届高三下学期期中教学质量检测数学试卷
名校
解题方法
2 . 已知椭圆
上有一点P到右焦点的距离为4,则点P到左焦点的距离为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19c732a50945ba0d08a4e3e0c4796c74.png)
A.6 | B.3 | C.4 | D.2 |
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2024-05-29更新
|
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2卷引用:陕西省榆林市第一中学2023-2024学年高二上学期期中考试数学试题
解题方法
3 . 已知椭圆
,A,B为左右两个顶点,
,
为左右两个焦点,O为原点,P为椭圆上一点,则( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ddce8b513016e50009c72e49708faed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
A.![]() |
B.![]() ![]() |
C.若直线l过点![]() ![]() |
D.若![]() ![]() |
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4 . 已知
是椭圆
的两个焦点,点
在
上,若
,则
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ee9ce51f55008258322bbe19810f62d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab7cfd750f35e1d26120cdd7dbfe4e8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e6eec892b6388fc223cff6752aac01.png)
A.8 | B.6 | C.20 | D.10 |
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5 . 已知椭圆C:
的左焦点为F,点P是C上任意一点,则
的值可能是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55b939a0c044b842cdc258e516a6d1de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ac654a052f98d1ccb7fede1f122cec3.png)
A.1 | B.3 | C.6 | D.8 |
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2023-12-09更新
|
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3卷引用:甘肃省金昌市永昌县第一高级中学2023-2024学年高二上学期期中数学试题
6 . 已知椭圆
的左焦点为
,
为
的上顶点,
,
是
上两点.若
,
,
构成以
为公差的等差数列,
的延长线与
的另一个交点为
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a92f7addc2ba3dcbe2d5f9751cc7fd08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4522fdddbca40f55f3130c4c44e0bb62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03e944586ad3d14e01f4d1ad9d8f4910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6459134d1c08c0307d38966e40473f4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfe9369621149328a9e5629bc5314604.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
A.当![]() ![]() |
B.![]() ![]() |
C.当![]() ![]() ![]() ![]() ![]() |
D.当![]() ![]() ![]() ![]() ![]() |
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解题方法
7 . 设椭圆
的左右焦点为
,
,P是C上的动点,则下列结论正确的是( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ee9ce51f55008258322bbe19810f62d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
A.P到![]() ![]() | B.![]() |
C.![]() | D.P到![]() |
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8 . 椭圆
上的一点到两个焦点的距离之和为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc439302e947dd0a1b4eb36eada91b12.png)
A.![]() | B.4 | C.8 | D.6 |
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9 . 设 P 是椭圆
上一点,F1、F2是椭圆的焦点,若
等于 4,则
等于( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a3d496386d3778a783a5b37726704ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4ef569668e797b1e94257fd5f4384dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96fa27f8db6167d4802a510371077bb5.png)
A.1 | B.2 | C.4 | D.6 |
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10 . 已知椭圆C:
的左、右焦点分别为
,
,点P为椭圆C上一动点,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/914075a4574c09bdb860d8f8f09a4e7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
A.椭圆C的离心率为![]() | B.![]() |
C.![]() | D.存在点P,使得![]() |
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2023-11-28更新
|
1161次组卷
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7卷引用:黑龙江省龙东五地市2023-2024学年高二上学期期中联考数学试题
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