2014·北京朝阳·一模
名校
1 . 已知椭圆
:
(
)经过点
,一个焦点为
.
(1)求椭圆
的方程;
(2)若直线
(
)与
轴交于点
,与椭圆
交于
、
两点,线段
的垂直平分线与
轴交于点
,求
的取值范围.
![](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/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d4f12a268aede3da12b0c123c8a28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd050ed2c70c403379758235904a2cd3.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6a7108d77b8ad681a6b7573ecac0406.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2c80c26a794a844127aae7dee87c93b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81f600e23b3e90cfa44bf6a3c3fb63a0.png)
您最近一年使用:0次
2020-12-06更新
|
487次组卷
|
9卷引用:天津市和平区2019-2020学年高二上学期期末数学试题
天津市和平区2019-2020学年高二上学期期末数学试题(已下线)2014届北京市朝阳区高三第一次综合练习文科数学试卷天津市第一中学2019届高三一月月考数学试题(一)(已下线)专题54 圆锥曲线大题解题模板-2021年高考一轮数学单元复习一遍过(新高考地区专用)(已下线)专题51 圆锥曲线大题解题模板-2021年高考一轮数学(文)单元复习一遍过浙江省“金兰教育合作组织”2018-2019学年高二下学期期中联考数学试题2023版 湘教版(2019) 选修第一册 过关斩将 第3章 专题强化练11 圆锥曲线中的最值与范围问题的解法2023届甘肃省高考数学模拟试卷(三)2023届甘肃省高考理科数学模拟试卷(三)
名校
2 . 已知椭圆
的离心率为
,过点
.
(Ⅰ)求椭圆C的标准方程;
(Ⅱ)设左、右焦点分别为
,经过右焦点F2的直线l与椭圆C相交于A、B两点,若
,求直线l方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c7316976a221c051a2c14df80b1347.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a812a9b58ccba331cfd21d244329af01.png)
(Ⅰ)求椭圆C的标准方程;
(Ⅱ)设左、右焦点分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da06c2b90eeded6e2f7566d076a76eba.png)
您最近一年使用:0次
2020-09-26更新
|
968次组卷
|
7卷引用:北京市平谷区2019-2020学年度高二年级下学期数学(期末)质量监控试题
名校
3 . 已知椭圆:
的焦距为
,其上下顶点分别为
、
,点
,
,
.
(1)求椭圆的方程;
(2)点P的坐标为
,过点A任意作直线
与椭圆相交于M、N两点,设直线
、
、
的斜率依次成等差数列,探究m、n之间是否满足某种数量关系,若是,请给出m、n的关系式,并证明;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3818e95641a272c1616f0cbd838c54e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2634cca127c335b9f66d88ccfb22d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c6ff81aedbefa935da289dc632e78eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a475d30f8a83feed0ed3c238bb24580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3699a53e328aa226ed929197352b9b36.png)
(1)求椭圆的方程;
(2)点P的坐标为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62202aafab8e78592209b8d2523f5be7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/279563c3c055777ce1aa369a2ef54aed.png)
您最近一年使用:0次
名校
4 . 如图,在平面直角坐标系xOy中,椭圆C:
(a>b>0)的离心率为
,短轴长是2.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/10/58863c5c-eb69-4084-a30c-d486fffbf732.png?resizew=181)
(1)求椭圆C的方程;
(2)设椭圆C的下顶点为D,过点D作两条互相垂直的直线l1,l2,这两条直线与椭圆C的另一个交点分别为M,N.设l1的斜率为k(k≠0),△DMN的面积为S,当
,求k的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/10/58863c5c-eb69-4084-a30c-d486fffbf732.png?resizew=181)
(1)求椭圆C的方程;
(2)设椭圆C的下顶点为D,过点D作两条互相垂直的直线l1,l2,这两条直线与椭圆C的另一个交点分别为M,N.设l1的斜率为k(k≠0),△DMN的面积为S,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f398ffe266e148d499d31864f45df6.png)
您最近一年使用:0次
2019-01-10更新
|
1054次组卷
|
2卷引用:天津市和平区耀华中学2019-2020学年高二上学期期末数学试题
5 . 已知椭圆
的方程为
(
)的离心率为
,圆
的方程为
,若椭圆
与圆
相交于
,
两点,且线段
恰好为圆
的直径.
(1)求直线
的方程;
(2)求椭圆
的标准方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc4ba9002be095fc2e55a954350c22f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
您最近一年使用:0次
6 . 直线
与椭圆
相切的充要条件是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97752154ca23b228ce862737afa7cabe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb9776de993951025bdcaac8c7cdff8e.png)
您最近一年使用:0次
名校
解题方法
7 . 已知椭圆
的中心在原点,离心率为
,右焦点到直线
的距离为2.
(1)求椭圆
的方程;
(2)椭圆下顶点为
,直线
(
)与椭圆相交于不同的两点
,当
时,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1174142f3bba761585b6bc2653009b36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48e307be89a2ae01bd3fb8442b4e12af.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)椭圆下顶点为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15b256345d7109e081b7c895591e995d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2c80c26a794a844127aae7dee87c93b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b485b62d004d52fb31d6ed99ccb7669.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2016-12-04更新
|
611次组卷
|
4卷引用:天津市和平区2017-2018学年高二上学期期末考试数学(文)试题