【题文】设集合,, ,若,则实数的取值范围是____________.
题型:难度:来源:
【题文】设集合
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322224421-67226.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322224421-53223.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322224422-86432.png)
,若
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322224422-73643.png)
,则实数
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322224422-31264.png)
的取值范围是____________.
答案
【答案】
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322224423-26369.png)
解析
【解析】
试题分析:由题可知,集合
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322224423-94789.png)
表示圆
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322224424-42390.png)
上点的集合,集合
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322224424-59537.png)
表示圆
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322224425-12489.png)
上点的集合,集合
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322224425-51336.png)
表示曲线
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322224425-11493.png)
上点的集合,此三集合所表示的曲线的中心都在
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322224426-26996.png)
处,集合
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322224423-94789.png)
、
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322224424-59537.png)
表示圆,集合
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322224425-51336.png)
则表示菱形,可以将圆与菱形的中心同时平移至原点,如图所示,可求得
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322224422-31264.png)
的取值范围是
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322224423-26369.png)
.
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322224427-42418.png)
考点:曲线与方程的实际应用问题.
举一反三
【题文】设全集
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322224318-51031.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322224318-42492.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322224318-16225.png)
,则图中阴影部分表示的集合为( )
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322224319-48250.jpg)
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