解题方法
1 . 已知椭圆
的长轴长为
,点
在椭圆
上.
(1)求椭圆
的方程;
(2)设
是经过椭圆
下顶点的两条直线,
与椭圆
相交于另一点
与圆
相交于另一点
,若
的斜率不等于0,
的斜率等于
斜率的3倍,证明:直线
经过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3be3354fbc3aecfdd295aee9b9c56191.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e95f7197eefaa30c63b73aef5ef464b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.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/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
您最近一年使用:0次
22-23高二上·山西晋中·期末
名校
解题方法
2 . 已知椭圆
过点
,
.
(1)求椭圆
的标准方程;
(2)若点
是圆
上的一点,过点
作圆
的切线交椭圆
于
,
两点,证明:以
为直径的圆过原点
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6b0dadb875cccce870b69409a476606.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96d695c07baa4ccb21b5958f027df013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee8f55df5f7dd9f01b6e1246409d9e5c.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/441005b2d2555617abbb8ab2c4d36edf.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/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/1dde8112e8eb968fd042418dd632759e.png)
您最近一年使用:0次
2023-02-04更新
|
482次组卷
|
7卷引用:山西省平遥中学校2022-2023学年高二上学期期末考试数学试题
(已下线)山西省平遥中学校2022-2023学年高二上学期期末考试数学试题山西省朔州市怀仁市第一中学校2022-2023学年高二下学期期末数学试题湖南省湘潭市2022-2023学年高二下学期期末数学试题(已下线)期末真题必刷常考60题(32个考点专练)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(人教A版2019选择性必修第一册)云南省曲靖市民族中学2022-2023学年高二下学期期中考试数学试题安徽省阜阳市第三中学2023-2024学年高二上学期一调考试(10月月考)数学试题(已下线)第五篇 向量与几何 专题4 极点与极线 微点2 圆锥曲线之极点与极线(二)
名校
3 . 已知椭圆
的左、右焦点分别为
,
,点
在椭圆C上,且满足
.
(1)求椭圆C的标准方程;
(2)设直线
与椭圆C交于不同的两点M,N,且
(O为坐标原点).证明:总存在一个确定的圆与直线l相切,并求该圆的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.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/1a5f4493abd2b69f83eae0362c509f1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df935e8d792fc386d11dd936f26427bf.png)
(1)求椭圆C的标准方程;
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fc5bd66dd6d5e09ff0893a938aed56e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c0b06dc01c30d13f64be2ac6a1d811e.png)
您最近一年使用:0次
2022-02-15更新
|
361次组卷
|
2卷引用:山西省怀仁市第一中学2021-2022学年高二上学期期末数学(理)试题
名校
解题方法
4 . 已知椭圆
经过点
,且椭圆的一个焦点为
.
(1)求椭圆
的方程;
(2)若以椭圆右顶点
为直角顶点的动直角三角形斜边端点
落在椭圆
上,求证:直线
过定点,并求出这个定点坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/981fe6f202c7a549a96230f49c11ab89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eb83069a218702b339623b83347e597.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)若以椭圆右顶点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
您最近一年使用:0次
2017高二·四川·期末
名校
解题方法
5 . 已知椭圆
:
经过点
,一个焦点
的坐标为
.
(1)求椭圆
的方程;
(2)设直线
:
与椭圆
交于
,
两点,
为坐标原点,若
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a5f4493abd2b69f83eae0362c509f1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fab8a0cc6504aa4c3a38006f5394b4c2.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15b256345d7109e081b7c895591e995d.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3af31ea41c95a92aeda98e30d065635.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ace585d3cc2e113a0927cdf9e56756a.png)
您最近一年使用:0次
2020-09-21更新
|
884次组卷
|
10卷引用:山西省汾阳市2020-2021学年高二上学期期末数学(理)试题
山西省汾阳市2020-2021学年高二上学期期末数学(理)试题(已下线)四川省遂宁市2016-2017学年高二下学期期末考试数学(理)试题四川省遂宁市2016-2017学年高二下学期期末教学水平监测数学(理)试题四川省遂宁市2016-2017学年高二下学期期末考试数学(理)试题江西省南昌市第二中学2017-2018学年高二下学期第一次月考数学(文)试题【全国百强校】四川省棠湖中学2017-2018学年高二下学期期中考试数学(理)试题【全国百强校】四川省棠湖中学2017-2018学年高二下学期期中考试数学(文)试题四川省新津中学2020-2021学年高三上学期开学考试数学(理)试题(已下线)专题40 圆锥曲线中参数范围与最值问题-2(已下线)重难点突破17 圆锥曲线中参数范围与最值问题(八大题型)
名校
6 . 已知椭圆C:
1(a>b>0)的离心率e
,且点P(
,1)在椭圆C上.
(1)求椭圆C的方程;
(2)若椭圆C的左焦点为F,右顶点为A,点M(s,t)(t>0)是椭圆C上的动点,直线AM与y轴交于点D,点E是y轴上一点,EF⊥DF,EA与椭圆C交于点G,若△AMG的面积为2
,求直线AM的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d22ecb9b0a87ab5098571bdf80441231.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b945ef245f4e808511e0069fa05ed6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e051d14fd6a787387995331f5e6d026.png)
(1)求椭圆C的方程;
(2)若椭圆C的左焦点为F,右顶点为A,点M(s,t)(t>0)是椭圆C上的动点,直线AM与y轴交于点D,点E是y轴上一点,EF⊥DF,EA与椭圆C交于点G,若△AMG的面积为2
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e051d14fd6a787387995331f5e6d026.png)
您最近一年使用:0次
2020-03-15更新
|
787次组卷
|
4卷引用:山西省五地市2019届高三上学期期末联考数学(理)试题