名校
解题方法
1 . 已知椭圆
的离心率为
,长轴的一个顶点为
,短轴的一个顶点为
,
为坐标原点,且
.
(Ⅰ)求椭圆
的标准方程;
(Ⅱ)直线
与椭圆
交于
两点,且直线
不经过点
.记直线
的斜率分别为
,试探究
是否为定值.若是,请求出该定值,若不是,请说明理由.
![](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/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/7a179d4b64e0be2bfda5d9df241ec276.png)
(Ⅰ)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(Ⅱ)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d00a5df9d281dd4e1e45bf6a4d6fb27.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274f07eccbd7406ec7d330389a7b5ebd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/592b4967f670b263ea9331370bc46940.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b69e3f7ddd51215d00661c09cd900d60.png)
您最近一年使用:0次
2017-09-03更新
|
998次组卷
|
2卷引用:北京八一学校2022届高三上学期开学考试数学试题
名校
2 . 设
分别为椭圆
的左、右焦点,点
为椭圆
的左顶点,点
为椭圆
的上顶点,且
.
(Ⅰ)若椭圆
的离心率为
,求椭圆
的方程;
(Ⅱ)设
为椭圆
上一点,且在第一象限内,直线
与
轴相交于点
,若以
为直径的圆经过点
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/367e9b549284f968fc0c5ec84f36b01a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/f371c0b1d573c06516ab1904d95ee49f.png)
(Ⅰ)若椭圆
![](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/2a30f3a8b673cc28bd90c50cf1a35281.png)
(Ⅱ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c83e02c09428538ce8ae136cff26d3f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9907e6a950f123fa42754880f010b978.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9ab3f6fa3a714f0592c72c283b34b11.png)
您最近一年使用:0次
2016-12-03更新
|
929次组卷
|
3卷引用:北京市北京八中2018届高三第二次月考数学理科试题