题目
题型:不详难度:来源:
已知椭圆方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180025-37684.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180025-59196.gif)
(Ⅰ)求证直线AB的斜率为定值;
(Ⅱ)求△
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180025-90172.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180026-54842.gif)
直线MA方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180026-62764.gif)
分别与椭圆方程联立,可解出
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180026-77994.gif)
同理得,直线MB方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180026-20976.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180027-72775.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180027-53929.gif)
(Ⅱ)设直线AB方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180027-44511.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180025-37684.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180027-69534.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180028-95224.gif)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180028-91561.gif)
点M到AB的距离为
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180028-91455.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180028-92900.gif)
设△AMB的面积为S. ∴
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180029-45533.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180029-58982.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180029-98245.gif)
解析
核心考点
试题【(本小题满分12分)已知椭圆方程为,射线(x≥0)与椭圆的交点为M,过M作倾斜角互补的两条直线,分别与椭圆交于A、B两点(异于M).(Ⅰ)求证直线AB的斜率为定】;主要考察你对椭圆的定义与方程等知识点的理解。[详细]
举一反三
已知椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180019-28729.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180019-70973.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180019-39478.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180020-89312.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180020-73425.gif)
(Ⅰ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180020-48696.gif)
(Ⅱ)若直线y=kx(k<0)与
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180020-48696.gif)
设椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175959-11042.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175959-36663.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175959-94629.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175959-56855.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180000-69890.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180000-82206.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180000-35047.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180000-41436.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180001-27911.gif)
(I)求
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180001-92531.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175959-11042.gif)
(II)过
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180001-88467.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180001-26208.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180001-15827.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180002-78798.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180002-39394.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180003-65542.gif)
求四边形
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180003-30219.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023180004-83627.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175950-87057.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175950-12132.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175950-65072.gif)
(Ⅰ)求椭圆的方程;
(Ⅱ)过点
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175950-89481.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175951-83948.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175951-48037.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175951-14712.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175951-36283.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175951-83948.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175937-64892.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175938-96737.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175938-41470.gif)
(1)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175938-51970.gif)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175938-36841.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175938-51970.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175938-16893.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175939-40989.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175939-31537.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175939-40808.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175938-51970.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175938-36841.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175940-83943.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175940-45826.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175940-85038.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175939-40808.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175938-51970.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175940-70266.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175917-29275.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175917-71376.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175917-15485.gif)
(1)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175917-74468.gif)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175918-60104.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175917-74468.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175918-63758.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175917-74468.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175918-60104.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175918-56627.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175918-86567.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175919-28119.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175919-18976.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191023/20191023175919-82481.gif)
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