名校
解题方法
1 . 椭圆C:
的左、右焦点分别为
,
,过
且斜率为
的直线与椭圆交于A,B两点(A在B左侧),若
,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/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1c58171a47ab1f8895487636ee275fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/555feca84fa8baa4ec234b65610d76fa.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2卷引用:广东省广州市执信中学2024届高三下学期教学情况检测(三)数学试题
2 . 已知椭圆
的左、右焦点分别是
,其离心率
,过
且垂直于
轴的直线被椭圆
截得的线段长为1.
(1)求椭圆
的方程;
(2)点
是椭圆
上除长轴端点外的任一点,过点
作斜率为
的直线
,使得
与椭圆
有且只有一个公共点,设直线
的斜率分别为
,若
,证明:
为定值,并求出这个定值;
(3)点
是椭圆
上除长轴端点外的任一点,设
的角平分线
交椭圆
的长轴于点
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/323227dd8a7a31c078eac609b9acf472.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c38928a92bc4b44ed3c9b89769f5372.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5de85df85401e7e8da683ea4a784963c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)点
![](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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/587662afaaecad25c6f5f9e5e7ff28b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42623f14667ebfa914eb12d026023d6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2c80c26a794a844127aae7dee87c93b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0fe8d1be8a033e33fcc111cdbcf7b04.png)
(3)点
![](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/c94fe48bf7af022ecbbe13833fdcc2c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b62769b7177ef4bc952dc1dd51d6b510.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2024-03-25更新
|
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2卷引用:广东省惠州市华罗庚中学2023-2024学年高二下学期3月月考数学试题
名校
3 . 在平面直角坐标系中,已知椭圆
的左、右焦点分别为
、
,点A在椭圆E上且在第一象限内,
,点A关于y轴的对称点为点B.
(1)求A点坐标;
(2)在x轴上任取一点P,直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/857f5e7c24364ed4b52896bd1b12d453.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5215b714cde3ed7790b3ed4f6711c3.png)
(3)设点M在椭圆E上,记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a11cb104b04c4e6a1be700e81da279a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8060a00d925f27135a7baff2d0e9d598.png)
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名校
解题方法
4 . 在平面直角坐标系中,,
,M为平面内的一个动点,满足:
.
(1)求动点M的轨迹C的方程;
(2)设动直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fc5bd66dd6d5e09ff0893a938aed56e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d6b62523a312bd8c09db0c3d9c930c1.png)
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2024-03-22更新
|
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|
2卷引用:广东省燕博园2024届高三下学期3月综合能力测试(CAT联考)数学试题
5 . 已知椭圆
的左右焦点分别为
,
,其长轴长为6,离心率为e且
,点D为E上一动点,
的面积的最大值为
,过
的直线
,
分别与椭圆E交于A,B两点(异于点P),与直线
交于M,N两点,且M,N两点的纵坐标之和为11.过坐标原点O作直线
的垂线,垂足为H.
(1)求椭圆E的方程;
(2)问:平面内是否存在定点Q,使得
为定值?若存在,请求出Q点坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.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/7bb4e5ce81ff39f0a3d29625f5835d7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4df8816403d7f16b505ffc4a3574204d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18f4ec943ad1319d9df9ead145195817.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/224d30ca84f1aeeeda7a718e751a4925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(1)求椭圆E的方程;
(2)问:平面内是否存在定点Q,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/636af55f0a84e603305e628041375a0c.png)
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2卷引用:广东省广州市第六中学2023-2024学年高二下学期期中考试数学试题
6 . “
”是“方程
表示的曲线为椭圆”的( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54323f3dc8905f56acf5da29b6847b47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecb8e84574016c96442fe82369d2e62c.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 |
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|
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3卷引用:广东省2024届高三数学新改革适应性训练七(九省联考题型)
广东省2024届高三数学新改革适应性训练七(九省联考题型)江西省宜春市丰城市第九中学日新班2023-2024学年高二21、22班上学期期末考试数学试题(已下线)专题06集合与常用逻辑用语、不等式期末6种常考题型归类【好题汇编】-备战2023-2024学年高二数学下学期期末真题分类汇编(人教B版2019)
名校
7 . 命题
方程
表示焦点在
轴上的椭圆,则使命题
成立的充分必要条件是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51441c8788ff11be766766227793246d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a349f402f04751e4fc48903ca9366310.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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|
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3卷引用:广东省汕头市金山中学2023-2024学年高二上学期期末考试数学试题
名校
解题方法
8 . 已知椭圆E:
过点
,且其离心率为
.
(1)求椭圆E的方程;
(2)过点
的斜率不为零的直线与椭圆E交于C,D两点,A,B分别为椭圆E的左、右顶点,直线AC,BD交于一点P,M为线段PB上一点,满足
,问
是否为定值,若是,求出该定值;若不是,说明理由(O为坐标原点).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c453894bbede5be3f254614050b79c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
(1)求椭圆E的方程;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a2a5e336b6bcba6354fd366c892dd06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12352953fcc899f4f5591b4a82edc4a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/831d25950602b60473f0b819c78c22c7.png)
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4卷引用:广东省广州市番禺区2023-2024学年高二下学期期中数学试卷
9 . 在平面直角坐标系
中,已知点
,
,记
的轨迹为
.
(1)求
的方程;
(2)过点
的直线
与
交于
两点,
,
,设直线
的斜率分别为
.
(i)若
,求
;
(ii)证明:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/871868260c78a20767eae39bcdb97476.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eed5b1b5a80e66f5a6cd08be019376c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7a999c36de5c9a9ce876a4a56fa34c.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/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/913f78382630e50543e5f7192cae3ed3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c850811ba59a05e945a665196539a048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a16143ae1edcef852e367f50db8869f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dca1726d463bd741c904abd9b6589056.png)
(i)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e607c2f7ae494246768832acb0d54a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbf434334b09cc0fdd4e86e84e6ceb00.png)
(ii)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3342ecc389773431bc3f64410e41191.png)
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4卷引用:广东省两阳中学2023-2024学年高二下学期月考一数学试题
10 . 在直角坐标系
中,已知
.
(1)求点P的轨迹C的方程;
(2)设直线l不过坐标原点且不垂直于坐标轴,l与C交于A、B两点,点
为弦AB的中点.过点M作l的垂线交C于D、E,N为弦DE的中点.
①证明:l与ON相交;
②已知l与直线ON交于T,若
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b79a478ed91942ce279cd544dc2367f.png)
(1)求点P的轨迹C的方程;
(2)设直线l不过坐标原点且不垂直于坐标轴,l与C交于A、B两点,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26f3e91cf4f83b15d04eb8692034c379.png)
①证明:l与ON相交;
②已知l与直线ON交于T,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e72152ea8322f9b111ff39f4addae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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