题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225221-49429.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225221-88064.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225221-40491.png)
抛物线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225221-91826.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225222-86396.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225222-36160.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225222-93901.png)
(2)求满足
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225222-48232.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225222-90492.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225223-99979.png)
解析
试题分析:(1)抛物线与直线联立.由向量的数量积结合利用韦达定理可得结论.(2)根据向量的相等得到点M关于A,B两点的坐标关系,再由第一步的韦达定理消去k值即可.但要注意轨迹的范围.本题主要就是抛物线与直线的知识.向量知识在解析几何中的应用.
试题解析:解:将
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225223-69194.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225223-82041.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225224-38177.png)
因为动直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225224-30242.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225224-66388.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225224-46393.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225225-28832.png)
解得:
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225225-51916.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225224-66388.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225225-57629.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225225-89930.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225226-83195.png)
(1)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225222-36160.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225222-93901.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225226-50926.png)
=
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225226-49043.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225226-94211.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225222-36160.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225222-93901.png)
(2)解:
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225227-94095.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225227-50346.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225227-72494.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225227-52605.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225228-27747.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225228-33384.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225228-90879.png)
又由
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225225-51916.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225224-66388.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225229-67176.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225229-21449.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225229-31370.png)
所以,点
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225229-59003.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225223-99979.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225206-81592.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225206-28571.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225206-76817.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225206-28571.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225207-68266.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225207-23731.png)
(1)求椭圆方程;
(2)过点
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225207-97628.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225208-24175.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225208-86875.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225208-57950.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225208-46738.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225155-37108.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225155-82708.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225155-28053.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225155-18404.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225156-81299.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225156-58158.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225156-50249.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225156-19816.png)
A.1 | B.![]() | C.![]() | D.2 |
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225141-73965.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225141-23620.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225141-10518.png)
(1)求双曲线C的方程;
(2)已知直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225141-39144.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225126-37481.png)
(1)求动点P的轨迹方程;
(2)设直线AP和BP分别与直线x=3交于点M,N,问:是否存在点P使得△PAB与△PMN的面积相等?若存在,求出点P的坐标;若不存在,说明理由.
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225111-12036.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025225112-43066.png)
(1)求此椭圆的标准方程;
(2)在(1)中求过点F(2,0)的弦AB的中点M的轨迹方程.
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