题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234645-94174.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234645-18731.png)
(Ⅰ)若点G的横坐标为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234645-71177.png)
(Ⅱ)记△GFD的面积为S1,△OED(O为原点)的面积为S2.
试问:是否存在直线AB,使得S1=S2?说明理由.
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234645-75377.png)
(Ⅱ)不存在直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234645-43429.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234646-44576.png)
解析
试题分析:(Ⅰ)依题意,直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234645-43429.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234646-10244.png)
将其代入
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234646-44852.png)
整理得
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234646-25909.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234647-34570.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234647-56085.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234647-31868.png)
故点
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234647-34305.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234648-57314.png)
依题意,得
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234648-24846.png)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234645-75377.png)
(Ⅱ)解:假设存在直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234645-43429.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234646-44576.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234645-43429.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234648-59708.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234649-18221.png)
由(Ⅰ)可得
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234649-15016.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234649-62313.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234649-99022.png)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234650-67811.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234650-77318.png)
因为 △
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234650-39971.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234650-59434.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234651-77018.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234651-83364.png)
整理得
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234651-98906.png)
因为此方程无解,所以不存在直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234645-43429.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234646-44576.png)
点评:中档题,曲线关系问题,往往通过联立方程组,得到一元二次方程,运用韦达定理。本题(2)利用弦长公式,确定得到三角形面积表达式,实现对“存在性问题”的研究。
核心考点
试题【如图,已知椭圆的左焦点为F,过点F的直线交椭圆于A、B两点,线段AB的中点为G,AB的中垂线与x轴和y轴分别交于D、E两点.(Ⅰ)若点G的横坐标为,求直线AB的】;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/20191025/20191025234638-45329.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234638-25433.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234638-69971.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234639-96372.png)
(Ⅰ) 求曲线C的直角坐标方程;
(Ⅱ) 求直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234638-45329.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234639-77316.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234626-30139.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234627-64244.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234627-27338.png)
(1)求抛物线的方程;
(2)已知
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234627-66634.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234627-96795.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234628-99475.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234628-61089.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234628-72071.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234628-44620.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234612-78486.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234612-21068.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234612-47688.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234613-77031.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234613-23448.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234613-80284.png)
(1)求椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234613-75282.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234613-88358.png)
(2) 在曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234613-88358.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234614-65526.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234614-58776.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234613-75282.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234614-43345.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234614-32320.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234614-60608.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234615-71057.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234615-23888.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234615-61559.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234616-74508.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234616-38640.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234605-21693.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234605-48901.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234605-44389.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234606-25772.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234606-45121.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234606-65555.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234559-51107.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025234600-79518.png)
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