题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225024-81095.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225024-72940.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225024-81095.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225024-82060.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225024-96602.png)
(Ⅰ)求椭圆方程;
(Ⅱ)若直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225025-35988.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225025-78008.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225025-93834.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225025-47385.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225026-63702.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225026-72723.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225026-17496.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225026-50652.png)
解析
试题分析:(Ⅰ)本小题通过告诉两个条件.到焦点最长和最短的焦半径,即可求得所求的椭圆方程.本小题的已知条件要记清不要混淆.(Ⅱ)本小题是直线与椭圆的关系,常用的方法就是联立方程,判别式大于零,韦达定理.再根据弦MN的中垂线恒过一点.根据中点,定点,斜率其中的两个条件所以可以写出垂直平分线的直线方程.再将另一个代入就可得到一个关于k,m的等式.再结合判别式得到不等式即可得到k的取值范围.本题的运算量较大些.要认真做到“步步为赢”.
试题解析:(I)由题意设椭圆的标准方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225027-89328.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225027-40964.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225027-21406.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225026-17496.png)
(Ⅱ)设
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225027-13334.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225027-68084.png)
消去
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225028-81182.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225028-46893.png)
∵直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225028-49192.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225028-17734.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225028-59898.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225029-17026.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225029-41971.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225029-88688.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225029-65253.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225025-47385.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225030-32056.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225030-31845.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225030-81285.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225030-32056.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225030-99585.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225031-57639.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225031-62381.png)
将上式代入得
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225031-72526.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225031-39699.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225031-58983.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225032-98514.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225032-17708.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225026-50652.png)
核心考点
试题【已知椭圆的中心在坐标原点,焦点在轴上,椭圆上的点到焦点距离的最大值为,最小值为.(Ⅰ)求椭圆方程;(Ⅱ)若直线与椭圆交于不同的两点、,且线段的垂直平分线过定点,】;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/20191025/20191025225018-40530.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225018-98991.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225018-40530.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225005-51416.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225005-95988.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225005-11974.png)
⑴求椭圆E的方程;
⑵设P是椭圆E上一点,过P作两条斜率之积为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225005-95988.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225005-65196.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225005-65196.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225005-75361.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224957-15258.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224957-61809.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224957-29347.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224957-15258.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224950-17104.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224950-70459.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224950-95865.png)
(1)求抛物线的标准方程;
(2)若抛物线与直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224950-91807.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224950-98390.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224951-83116.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224951-80170.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224936-91626.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224936-37704.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224936-79650.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224937-32146.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224937-69753.png)
(1)求椭圆方程;
(2)点
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224937-60398.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224937-20436.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224938-10100.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224937-60398.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224937-20436.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224938-10100.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224938-78799.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224937-32146.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224938-78799.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224938-70806.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224938-70806.png)
(3)过椭圆的上顶点作互相垂直的两条直线分别交椭圆于另外一点
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224938-62466.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224938-37552.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025224939-94221.png)
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