题目
题型:不详难度:来源:
己知双曲线的中心在原点,右顶点为
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042716-27194.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042716-53685.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042717-99639.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042717-59850.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042717-10177.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042717-72502.gif)
(Ⅰ)若直线
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042717-72502.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042717-75956.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042718-67934.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042717-10177.gif)
(Ⅱ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042718-61382.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042718-35740.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042718-63601.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042717-59850.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042717-72502.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042719-80990.gif)
由点
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042719-36995.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042717-72502.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042719-89396.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042719-51026.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042720-10970.gif)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042720-84146.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042720-40871.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042720-92922.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042721-69747.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042721-71971.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042721-55604.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042721-15612.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042721-14755.gif)
(Ⅱ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042718-61382.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042722-67150.gif)
由于点
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042722-20438.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042717-72502.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042719-89396.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042717-72502.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042722-76731.gif)
因为点
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042722-20438.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042722-67496.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042722-91500.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042723-40814.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042723-80043.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042723-18695.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042723-40814.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042723-84500.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042724-79682.gif)
所以点
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042723-84500.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042724-68546.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042722-91500.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042724-84678.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042724-52184.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042717-72502.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042725-44502.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042725-52612.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042722-91500.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042725-13567.gif)
设双曲线方程为:
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042725-70243.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042725-16214.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042726-84557.gif)
所以双曲线方程为:
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042726-97239.gif)
解析
核心考点
试题【(本小题满分12分)己知双曲线的中心在原点,右顶点为(1,0),点.Q在双曲线的右支上,点(,0)到直线的距离为1.(Ⅰ)若直线的斜率为且有,求实数的取值范围;】;主要考察你对双曲线的定义与方程等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042712-83985.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042712-52688.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042712-82398.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042709-72407.jpg)
A.1 | B.![]() | C.![]() | D.2 |
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042700-73471.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042700-88344.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042700-11271.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042700-51435.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042701-78810.gif)
(1)求双曲线的方程;
(2)直线
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042701-13234.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042701-27377.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042701-27377.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042701-43761.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042702-25915.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042654-65916.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042654-11292.gif)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042647-12454.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042647-66965.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042647-39651.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024042647-45026.gif)
A.充分不必要条件 | B.必要不充分条件 |
C.充要条件 | D.既不充分也不必要条件 |
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