题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233625-70643.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233625-58968.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233625-45981.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233625-68278.png)
A.![]() ![]() | B.![]() |
C.![]() | D.(-∞,-3]∪![]() |
答案
解析
试题分析:设P(t,t2-1),Q(s,s2-1),∵BP⊥PQ,
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233626-60479.png)
即t2+(s-1)t-s+1=0
∵t∈R,P,Q是抛物线上两个不同的点,∴必须有△=(s-1)2+4(s-1)≥0.
即s2+2s-3≥0,解得s≤-3或s≥1.
∴Q点的横坐标的取值范围是 (-∞,-3]∪[1,+∞),故选D。
点评:中档题,解题的关键是利用斜率之积为-1构建方程,再利用方程根的判别式大于等于0进行求解
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233616-12931.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233608-46047.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233608-86879.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233609-75126.png)
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![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233610-91809.png)
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![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233601-87968.png)
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![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233602-33954.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233602-83087.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233602-83087.png)
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![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233601-44202.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233603-69132.png)
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![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233556-50127.png)
(Ⅰ)求该双曲线方程 ;
(Ⅱ)若直线m经过该双曲线的右焦点且斜率为1,求直线m被双曲线截得的弦长.
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233542-97979.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233543-81628.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233543-81628.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233543-81881.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233543-87766.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233543-23241.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233544-29784.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233544-99007.png)
(Ⅰ)求该椭圆的离心率;
(Ⅱ)设线段
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233543-23241.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233544-49302.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233543-23241.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233545-29846.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233545-29862.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233545-94682.png)
记△
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233546-58884.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233546-81957.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025233546-23006.png)
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