题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225504-83409.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225504-27652.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225504-12584.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225504-27652.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225505-26134.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225505-50903.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225505-73127.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225505-38537.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225506-74310.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225506-40667.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225506-19152.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225506-77652.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225507-62329.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225507-48653.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225507-15670.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225507-29048.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225508-66758.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225508-12926.jpg)
(1)求以
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225508-23820.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225508-46990.png)
(2)根据条件可判定点
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225508-66758.png)
(3)设线段
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225505-38537.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225509-12625.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225509-26639.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225509-67783.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225506-40667.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225509-12625.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225510-94299.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225510-43430.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225510-74948.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225511-34091.png)
解析
试题分析:根据长轴长
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225511-57481.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225511-55758.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225512-98884.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225506-19152.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225512-13194.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225512-23572.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225512-23572.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225510-43430.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225511-34091.png)
试题解析:
根据题意可知,椭圆的焦点在
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225504-12584.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225512-82294.png)
因为长轴长
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225511-57481.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225511-55758.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225513-30847.png)
所以所求的椭圆的标准方程为:
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225510-74948.png)
由题意知,
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225513-26156.png)
可得直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225506-19152.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225513-98428.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225512-13194.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225513-71750.png)
联立可解得其交点
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225514-89284.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225512-23572.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225510-74948.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225512-23572.png)
另法:设直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225506-19152.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225506-77652.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225514-36966.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225514-46060.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225514-29952.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225515-46118.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225515-23713.png)
①②相乘,整理可得
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225515-82281.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225515-84772.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225515-29383.png)
所以L在椭圆上.
(3)类比(2)的结论,即可得到直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225510-43430.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225511-34091.png)
核心考点
试题【矩形的中心在坐标原点,边与轴平行,=8,=6.分别是矩形四条边的中点,是线段的四等分点,是线段的四等分点.设直线与,与,与的交点依次为.(1)求以为长轴,以为短】;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
A.![]() | B.![]() | C.![]() | D.![]() |
(Ⅰ)求椭圆C的标准方程;
(Ⅱ)若直线l:
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225449-94840.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225440-43854.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225440-58004.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225431-42509.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225431-87125.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225432-95769.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225432-48143.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225420-99189.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225420-32404.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225421-21791.png)
(Ⅰ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225421-42536.png)
(Ⅱ)求△ABM面积
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225421-79632.png)
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