题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013509-81884.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013509-22880.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013509-80514.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013509-98196.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013510-24146.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013510-52805.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013510-32485.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013510-44369.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013510-55546.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013510-59707.png)
(Ⅰ)若弦
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013509-22880.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013510-94043.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013509-22880.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013511-76647.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013509-22880.png)
(Ⅱ)若弦
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013509-81884.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013511-47220.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013509-22880.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013511-68850.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013509-22880.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013511-58898.png)
解析
试题分析:(Ⅰ)由题意得:直线
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013509-22880.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013511-74357.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013511-30170.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013511-12938.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013512-73604.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013512-54436.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013512-84947.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013512-61324.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013512-44588.png)
故满足题意的直线
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013509-22880.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013511-68850.png)
(Ⅱ)解法一:由(Ⅰ)得:圆
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013512-54904.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013513-70757.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013513-46623.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013513-32344.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013513-19787.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013513-24461.png)
∵点
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013510-52805.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013512-54904.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013513-77992.png)
∵点
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013510-32485.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013514-35722.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013514-96346.png)
联立方程①②解得:
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013514-90873.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013514-16236.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013515-94543.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013515-15019.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013509-81884.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013511-47220.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013515-59041.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013515-27028.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013515-49389.png)
化简得
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013516-14587.png)
直线
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013509-22880.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013516-76736.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013516-43432.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013516-81235.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013516-14587.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013509-22880.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013516-43432.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013517-23956.png)
∴弦
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013509-22880.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013511-58898.png)
解法二:由(Ⅰ)得:圆
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013512-54904.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013513-46623.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013513-32344.png)
∵圆
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013512-54904.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013517-12283.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013514-35722.png)
又端点
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013510-52805.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013510-32485.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013510-44369.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013510-55546.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013515-94543.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013515-15019.png)
由弦
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013509-81884.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013511-47220.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013509-22880.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013511-58898.png)
∵弦
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013509-81884.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013511-47220.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013515-59041.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013515-27028.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013515-49389.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013517-40133.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013517-88314.png)
由①得
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013517-32453.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013518-43071.png)
∴弦
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013509-22880.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013511-58898.png)
点评:本题以直线、圆、椭圆为载体,综合考查推理论证能力、数形结合思想、化归与转化思想、函数与方程思想.
核心考点
试题【如图,设、分别是圆和椭圆的弦,且弦的端点在轴的异侧,端点与、与的横坐标分别相等,纵坐标分别同号.(Ⅰ)若弦所在直线斜率为,且弦的中点的横坐标为,求直线的方程;(】;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/20191026/20191026013457-97338.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013457-95026.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013458-94513.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013458-40296.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013458-68182.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013458-94513.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013448-76556.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013448-64042.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013448-29357.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013448-51394.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013440-10426.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013440-63522.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013441-89327.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013440-10426.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013423-32632.png)
求焦点为(-5,0)和(5,0),且一条渐近线为
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026013417-42491.png)
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