题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014000-74291.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014000-30766.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014000-10040.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014001-43816.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014001-54858.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014001-35232.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014001-50126.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014002-41661.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014002-58452.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014000-10040.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014002-60489.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014002-10223.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014003-80266.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014002-60489.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014000-10040.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014003-78433.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014003-73567.png)
(Ⅰ) 求椭圆C的方程;
(Ⅱ) 是否存在点
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014002-10223.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014003-60139.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014003-54359.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014002-10223.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014004-17207.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014002-10223.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014004-74786.png)
解析
试题分析:(Ⅰ) 设
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014004-48198.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014005-27909.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014005-46566.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014005-71194.png)
因为离心率e=
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014005-67050.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014005-47599.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014006-66249.png)
所以椭圆C的方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014004-17207.png)
(Ⅱ) 当直线
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014002-60489.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014006-31217.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014002-60489.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014006-31217.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014006-39896.png)
此时
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014006-32627.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014007-48083.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014007-28222.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014007-96625.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014007-22374.png)
当直线
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014002-60489.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014006-31217.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014002-10223.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014006-39896.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014008-48989.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014008-48989.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014002-60489.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014008-96666.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014008-56190.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014008-93847.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014008-31899.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014009-96317.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014009-35509.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014003-60139.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014009-80351.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014003-60139.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014009-56807.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014009-35733.png)
联立
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014010-60618.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014010-35240.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014010-99301.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014010-20757.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014011-79599.png)
由题意
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014011-16508.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014011-16508.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014011-85543.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014011-27798.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014011-34417.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014012-32110.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014012-88992.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014012-91467.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014002-10223.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014012-69710.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014012-91467.png)
综上,存在两点
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014002-10223.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014004-74786.png)
点评:设直线方程时,要考虑到直线方程斜率是否存在;对于探究性问题,可以先假设存在,再进行计算,如果能求出来,就说明存在,如果求不出来或者得出矛盾,则说明不存在.
核心考点
试题【(本题满分13分) 如图,是离心率为的椭圆,:()的左、右焦点,直线:将线段分成两段,其长度之比为1 : 3.设是上的两个动点,线段的中点在直线上,线段的中垂线】;主要考察你对曲线与方程的应用等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013950-76236.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013950-11626.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013950-97845.png)
(1)求该椭圆的标准方程;
(2)过椭圆的一个焦点且互相垂直的直线
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013950-88621.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013951-78132.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013951-67734.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013951-71736.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013951-61676.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013951-71736.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013945-62214.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013945-62214.png)
A.[-![]() ![]() | B.[-2 , 2 ] | C.[-1 , 1 ] | D.[-4 , 4 ] |
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013931-34291.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013931-82229.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013931-90545.png)
(Ⅰ)求双曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013931-90545.png)
(Ⅱ)过点
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013932-74526.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013932-51285.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013931-90545.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013932-35437.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013932-35437.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013931-90545.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013932-65281.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013933-14406.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013933-62677.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013933-99557.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013932-35437.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013922-87822.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013922-72069.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013922-57740.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013922-42530.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013923-23126.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013923-19622.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013923-18989.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013909-57155.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013909-11805.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013910-40088.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013910-52729.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013910-99088.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013910-61525.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013910-12117.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013910-60379.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013910-85920.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013910-40088.png)
(1) 求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013909-57155.png)
(2) 垂直于
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013911-74571.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013911-52779.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013909-57155.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013911-44438.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013911-16052.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013911-62087.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013912-13118.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013912-12088.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013911-52779.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013912-13118.png)
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