题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130305-50762.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130305-68767.gif)
轴上,点A在双曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130306-77905.gif)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130306-85761.gif)
(2)将矩形ABOC以B旋转中心,顺时针旋转90°后得到矩形FBDE,双曲线交DE于M点,交EF于N点,求△MEN的面积.
(3)在双曲线上是否存在一点P,使得直线PN与直线BC平行?若存在,请求出P点坐标,若不存在,请说明理由.
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130306-45209.jpg)
答案
∴AB=4…………………………………………………1分
∵点A在第一象限
∴A(2,4)……………………………………………2分
∵顶点A在双曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130306-30759.gif)
将A点代入双曲线函数中,得:即
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130307-93197.gif)
(2)∵矩形ABOC以B为旋转中心,顺时针旋转90°后得到矩形BDEF
∴点N、E纵坐标为2,点M、E横坐标为6………4分
∴将
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130307-11090.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130307-95938.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130308-35229.gif)
将
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130308-31059.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130307-95938.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130308-91073.gif)
∴M(6,
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130308-27746.gif)
∴EM=
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130309-23657.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130309-45070.gif)
(3)设直线BC的表达式为
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130309-45422.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130309-52871.gif)
∵B(2,0)、C(0,4)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130310-66679.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130310-52152.gif)
∴直线BC的表达式为
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130310-35757.gif)
若直线
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130311-55637.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130311-66850.gif)
把N(4,2)代入,得
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130311-37971.gif)
∴直线PN为
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130311-83979.gif)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130312-54006.gif)
得
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130312-44611.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130312-36276.gif)
∴P点的坐标为(1,8)……………………………………………12分
解析
核心考点
试题【(12分)如图,面积为8的矩形ABOC的边OB、OC分别在轴、轴的正半轴上,点A在双曲线的图象上,且AC=2.(1)求值;(2)将矩形ABOC以B旋转中心,顺时】;主要考察你对反比例函数定义等知识点的理解。[详细]
举一反三
(1)求点D的坐标;
(2)求经过点D的反比例函数解析式.
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130259-35515.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130247-33507.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130247-35995.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130247-90457.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017130239-14456.png)