题目
题型:贵州省期中题难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121958-30488.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121958-19180.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121958-53956.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121958-93047.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121959-41102.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121959-90391.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121959-78086.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121959-51485.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121959-10045.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122000-22159.png)
(I)求
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122000-94540.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122000-84064.png)
(II)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122000-16916.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122000-72685.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122000-89627.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122001-33037.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122001-65576.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122001-96433.png)
由坐标原点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122001-90931.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122001-92657.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122002-67886.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122002-87144.png)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122002-29340.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122003-74336.png)
(II)由(I)知椭圆的方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122003-83061.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122003-68888.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122003-79202.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122004-97335.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122004-92726.png)
故不妨设
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122004-53873.png)
整理得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122004-14594.png)
显然
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122004-23215.png)
由韦达定理有:
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122005-63054.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122005-58551.png)
①.假设存在点P,使
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122005-16262.png)
则其充要条件为:点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122005-94156.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122005-48943.png)
整理得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122005-84349.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122006-45642.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122006-48988.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122006-96508.png)
②将
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122006-40183.png)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122007-33053.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122007-13425.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122007-12868.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122007-22680.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122008-36462.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122008-68445.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023122008-19114.png)
核心考点
试题【已知椭圆的离心率为,过右焦点F的直线与相交于、两点,当的斜率为1时,坐标原点到的距离为 (I)求,的值; (II)上是否存在点P,使得当绕F转到某一位置】;主要考察你对椭圆等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121942-98249.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121942-97799.png)
(1)试求椭圆M的方程;
(2)若斜率为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121942-25117.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121942-47627.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121934-73589.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121934-96944.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121934-99319.png)
(Ⅰ)求椭圆的方程;
(Ⅱ)是否存在过点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121934-89576.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121935-96034.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121911-27342.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121911-24112.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121911-26406.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121911-70031.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121912-37852.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121912-22515.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121912-44677.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121912-52016.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121913-26670.png)
(1)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121913-41105.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121913-91126.png)
(2)过焦点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121913-26608.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121913-36899.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121914-59409.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121914-12583.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121914-17959.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121914-55769.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121915-31861.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121859-42991.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121859-88501.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121900-51550.png)
(Ⅰ)求椭圆方程
(Ⅱ)当右焦点在以线段CD为直径的圆E的内部,求实数m的范围
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121900-97140.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121848-41629.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121848-74639.png)
(1)求椭圆C的方程;
(2)求直线l的方程以及点M的坐标;
(3)是否存在过点P的直线l
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121848-87264.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121849-55766.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121849-29557.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121849-92009.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023121849-25705.png)
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