名校
解题方法
1 . 已知
是椭圆
的左,右顶点,点
与椭圆上的点的距离的最小值为1.
(1)求点
的坐标.
(2)过点
作直线
交椭圆
于
两点(与
不重合),连接
,
交于点
.
(ⅰ)证明:点
在定直线上;
(ⅱ)是否存在点
使得
,若存在,求出直线
的斜率;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8868e2ba4401d727f1bcb1f5483b48f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a10b671d71472e80e380d36fddc125d.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
(ⅰ)证明:点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
(ⅱ)是否存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42b58b9ecc79dde008ca42af27e644b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2024-04-16更新
|
2528次组卷
|
5卷引用:浙江省杭州市2024届高三下学期4月教学质量检测数学试题
解题方法
2 . 已知A,B分别为椭圆
的左右顶点,点
,
在椭圆
上.
(1)求椭圆
的方程;
(2)过点
且斜率不为零的直线
与椭圆
交于C,D两点,若直线AC与BD相交于点
,求证:点
在定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60a6613f85428c262b43be0d0cbfa8ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d2f9bae73ec13c7c1082eedec6dd94d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92a0d4c22734cac795de1e5c5fbefa87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
解题方法
3 . 已知椭圆
的离心率为
.其左、右顶点分别为
,上,下顶点分别为
,且四边形
的面积为4.
(1)求椭圆
的标准方程;
(2)过点
的直线与椭圆
交于
两点,直线
与
交于点
.求证:点
在定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/663368000ac90f582d12675aa2d1e832.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d3c185d7ca631989313f9d896a803d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92e5d91f4f631c580c155eba8c92bda4.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78e0b4cce429003557b051ea0fa2f7de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6670479a0083dd2dfd5ad55b47b1ab6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9399c9a2a31b0e3165aea2d6ccc4f7c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b06b75fb4e379ff3b99e68f40136cad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
名校
解题方法
4 . 已知椭圆的离心率为
,
为上顶点,
为左顶点,
为上焦点,且
.
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/990eaf5dbba84f199bdc438da81fcfa6.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/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2dca049735b45fb9b2533c68605eddc.png)
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名校
解题方法
5 . 已知椭圆
的上、下顶点分别是
,点P(异于
两点),直线PA与PB的斜率之积为
,椭圆C的长轴长为6.
(1)求C的标准方程;
(2)已知
,直线PT与椭圆C的另一个交点为Q,且直线AP与BQ相交于点D,证明点
在定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dc48b2f1fe89050e80db7369248c789.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b889efe020137b112bfafaa8e0becda4.png)
(1)求C的标准方程;
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f134c358bb5b5fa06c935a47c4ebf10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
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2024-02-04更新
|
361次组卷
|
5卷引用:河北省石家庄市部分重点高中2024届高三上学期期末数学试题
名校
解题方法
6 . 已知点A、
分别是椭圆
:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
的上、下顶点,
、
是椭圆的左、右焦点,
,
.
(1)求椭圆
的标准方程;
(2)过点
的直线与椭圆
交于不同两点
、
(
、
与椭圆上、下顶点均不重合),证明:直线
、
的交点在一条定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f82eb4ba631d0f50d848aa6e576b379.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/9ba7267be8fb3db5ec612fb9d8950239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84cef568cfe2fc12a4dec11533ada274.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b25e326fdf9e5456f48e8a99a069f379.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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
您最近一年使用:0次
名校
解题方法
7 . 已知椭圆
的离心率为
.
(1)求椭圆C的方程;
(2)当椭圆的焦点在x轴上时,直线
与椭圆的一个交点为P(点P不在坐标轴上),点P关于x轴的对称点为Q,经过点Q且斜率为
的直线与l交于点M,点N满足
轴,
轴,求证:点N在直线
上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6b4e6cff6a0d2d12b6725b50e1115c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
(1)求椭圆C的方程;
(2)当椭圆的焦点在x轴上时,直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb0d6d0cfe389abca252332223b5da17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a9e2fac8d4b7ae85f1034ae4cc7e8b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52cbeb9b1c1d637b903cf3e5c7f730f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4453837093274bcb899902a62955e42.png)
您最近一年使用:0次
2023-09-09更新
|
514次组卷
|
5卷引用:北京市2024届新高三入学定位考试数学试题
北京市2024届新高三入学定位考试数学试题北京市东直门中学2024届高三上学期开学考试数学试题(已下线)考点17 解析几何中的定点与定直线问题 2024届高考数学考点总动员(已下线)第04讲 拓展一:直线与椭圆的位置关系-【练透核心考点】2023-2024学年高二数学上学期重点题型方法与技巧(人教A版2019选择性必修第一册)(已下线)第三章 圆锥曲线的方程(知识归纳+题型突破)-2023-2024学年高二数学单元速记·巧练(人教A版2019选择性必修第一册)
解题方法
8 . 已知椭圆E:
经过点
,右焦点为
.
(1)求E的标准方程;
(2)已知A,B分别为E的上顶点和下顶点,过点
且斜率存在的直线l与E交于C、D两点,证明:直线AC与直线BD的交点M在定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f21c7162941d2b54ebafb1795599195.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be92f0e0012a7696c78e3e00513edefd.png)
(1)求E的标准方程;
(2)已知A,B分别为E的上顶点和下顶点,过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160d93f92089ef36f3dab809d3114b8.png)
您最近一年使用:0次
解题方法
9 . 已知椭圆
的离心率为
,左右顶点分别为A,B,G为C的上顶点,且
的面积为2.
(1)求椭圆C的方程;
(2)过点
的动直线与C交于M,N两点.证明:直线
与
的交点在一条定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bc727c642cbc2181476b7dd8eca471e.png)
(1)求椭圆C的方程;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00ed24bfcc37b79fe9ca61ed8fdf26ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
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2023·全国·模拟预测
10 . 已知在平面直角坐标系
中,抛物线
的焦点
与椭圆
的一个顶点重合,抛物线
经过点
,点
是椭圆
上任意一点,椭圆
的左、右焦点分别为
,且
的最大值为
.
(1)求椭圆
和抛物线
的标准方程;
(2)过抛物线
上在第一象限内的一点
作抛物线
的切线,交椭圆
于
两点,线段
的中点为
,过点
作垂直于
轴的直线,与直线
交于点
,求证:点
在定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56cde76467136421e939d9981e6022f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee1c96a487881b995de89287a84dc66.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94fe48bf7af022ecbbe13833fdcc2c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9cbb1eec186a57915e5aced5edce78c.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)过抛物线
![](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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307bd991211ec79b47a4be52933bb8e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
您最近一年使用:0次