题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083355-53911.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083355-84470.gif)
椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083356-12287.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083356-19275.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083356-46301.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083356-83142.gif)
(1)建立适当的直角坐标系,求椭圆的方程;
(2)若点E满足
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083356-76799.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083357-48705.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083357-38000.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083356-12287.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083357-21649.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083357-98937.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083358-27892.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083358-83019.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083358-25008.jpg)
解析
在RT
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083358-66713.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083358-77199.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083359-66458.gif)
设椭圆F的方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083359-40908.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083359-71513.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083359-31390.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083359-72378.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083400-34714.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083400-84004.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083400-51957.jpg)
(2) 由
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083356-76799.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083400-53941.gif)
当直线L斜率不存在时,不满足 设L的方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083401-61181.gif)
代入
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083401-48701.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083401-21341.gif)
则L与椭圆有两个不同公共点的充要条件为
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083402-41614.gif)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083402-19644.gif)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083402-32405.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083402-85526.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083357-98937.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083402-94114.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083403-34693.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083403-94801.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083402-94114.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083403-40416.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083403-17836.gif)
代入
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083402-19644.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083404-71600.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083404-79121.gif)
或者用点差法
核心考点
试题【如图,直角梯形中,椭圆以为焦点且过点,(1)建立适当的直角坐标系,求椭圆的方程;(2)若点E满足是否存在斜率的直线与椭圆交于两点,且,若存在,求的取值范围;若不】;主要考察你对线线角等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083349-51608.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083349-29673.gif)
A.![]() | B.![]() |
C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083343-31365.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083343-15223.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083343-82109.gif)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083344-93752.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083344-41310.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083344-98127.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083344-75116.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083345-70316.jpg)
(12)
A.∠PDA是侧面PDC与底面所成二面角的平面角 (13) | B.PC的长是点P到直线CD的距离 (14) | C.EF的长是点E到平面AFP的距离 (15) | D.∠PCB是侧棱PC与底面所成的线面角 |
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083339-29311.jpg)
(Ⅰ)求证:B1O⊥平面EAC;
(Ⅱ)若点
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083324-73066.gif)
(Ⅲ)求二面角B1-EA-C 的正弦值.
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022083324-98699.jpg)
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