题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042437-70964.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042437-89484.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042437-32826.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042438-54737.gif)
(Ⅰ)求r的取值范围
(Ⅱ)当四边形ABCD的面积最大时,求对角线AC、BD的交点P的坐标。
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042438-94542.jpg)
答案
(Ⅰ)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042438-62116.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042438-70595.gif)
解析
(Ⅰ)联立方程组
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042439-86711.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042439-97567.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042439-24917.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042439-57207.gif)
由此得到
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042440-21458.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042440-23260.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042438-62116.gif)
(Ⅱ)不妨设E与M的四个交点坐标分别为设
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042440-12350.gif)
直线AC,BD的方程分别为
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042440-12764.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042440-11213.gif)
解得点p的坐标为
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042441-95175.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042441-80963.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042441-27953.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042441-42288.gif)
由于四边形ABCD为等腰梯形,因而其面积
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042442-40701.gif)
将
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042442-33811.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042442-45730.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042442-38969.gif)
求导数,
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042442-93213.gif)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042443-30875.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042443-69459.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042443-20868.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042443-84385.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042443-52564.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042443-30875.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042444-87551.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042444-55349.gif)
当且仅当
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042443-52564.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042444-42049.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042438-70595.gif)
核心考点
试题【(22) (本小题满分12分)(注意:在试题卷上作答无效)如图,已知抛物线与圆相交于A、B、C、D四个点。(Ⅰ)求r的取值范围(Ⅱ)当四边形ABCD的面积最大时】;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
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042421-11907.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042421-22394.gif)
(1)求圆心
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042421-11907.gif)
(2)过点
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042421-76443.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042422-73461.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042422-97816.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042422-10539.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042422-97816.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042422-10539.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042422-11731.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042422-94918.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042423-54104.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042423-12934.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042411-63036.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042411-28249.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042411-55354.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042412-70075.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042412-99249.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042412-19580.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042412-85056.gif)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042406-68712.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042406-32619.gif)
A.
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042406-25822.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042407-74005.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042407-93125.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042407-67597.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042407-22773.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042352-26028.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042352-85671.gif)
(Ⅰ)求双曲线M的方程;
(Ⅱ)设直线
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042352-26435.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042353-25985.gif)
① 当
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042353-72760.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042353-66438.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042353-99885.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042354-34712.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042354-11052.gif)
② 是否存在这样的实数
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042353-72760.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042354-71008.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026042353-72760.gif)
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