题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002701-55078.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002701-82238.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002702-67273.png)
的渐近线方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002702-66687.png)
(1)求双曲线的标准方程;
(2) 过该双曲线的右焦点
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002702-72726.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002702-69878.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002703-97696.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002703-20517.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002703-60831.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002703-60910.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002703-92932.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002703-60910.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002704-95794.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002704-16707.png)
解析
试题分析:(1) 由题可知:
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002704-70663.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002704-28100.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002704-39311.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002705-53338.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002705-20170.png)
所求双曲线方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002704-95794.png)
(2)设过点
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002702-72726.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002705-87864.png)
联立方程组
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002705-81714.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002703-60831.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002706-48160.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002706-65871.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002706-43124.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002703-20517.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002707-43620.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002707-38107.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002707-53071.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002703-92932.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002707-19531.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002708-83249.png)
由②,③得
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002708-78665.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002708-88684.png)
由①,④得:
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002708-38682.png)
点评:本题考查双曲线方程的求法,考查双曲线的离心率和渐近线方程的求法.解题时要认真审
题,仔细解答,注意椭圆性质的合理运用.
核心考点
试题【双曲线与椭圆有相同的焦点,且该双曲线的渐近线方程为.(1)求双曲线的标准方程;(2) 过该双曲线的右焦点作斜率不为零的直线与此双曲线的左,右两支分别交于点、,设】;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/20191026/20191026002657-41720.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002658-75891.png)
A.5![]() | B.4![]() | C.3![]() | D.2![]() |
A.![]() | B.![]() |
C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002641-82187.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002641-43869.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002641-36581.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002622-43158.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002623-41064.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002623-97060.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002623-86232.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002623-27280.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002624-12931.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002624-48587.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002624-43729.jpg)
(1)若过
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002624-54110.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002625-43765.png)
(2)在(1)的条件下,过右焦点
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002625-14697.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002625-33108.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002625-59474.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002625-29950.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002623-27280.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002626-31509.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002626-75883.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002626-38779.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002616-39291.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026002616-80015.png)
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