题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034440-94569.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034440-39615.gif)
(1)求曲线C的方程;
(2)过点
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034440-41522.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034441-11395.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034441-44014.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034441-22520.gif)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034441-40730.gif)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034441-65348.gif)
∴点
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034441-16450.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034441-60341.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034441-54974.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034441-71926.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034441-22520.gif)
(2)当直线m的斜率不存在时,它与曲线C只有一个交点,不合题意,
设直线m的方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034441-37211.gif)
代入
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034441-62917.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034442-68376.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034442-33026.gif)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034442-12408.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034442-76991.gif)
点O到直线m的距离
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034442-22082.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034442-94210.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034442-89844.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034442-92646.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034442-94106.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034442-25533.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034443-39322.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034443-20888.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034443-61975.gif)
若
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034443-17593.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034444-73221.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034444-61457.gif)
若
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034444-97128.gif)
若
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034444-67791.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034441-40730.gif)
核心考点
试题【(本小题满分12分)已知曲线C上任意一点M到点F(0,1)的距离比它到直线 的距离小1.(1)求曲线C的方程;(2)过点当△AOB的面积为时(O为坐标原点),求】;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/20191026/20191026034434-69892.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034434-55983.gif)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034428-99220.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034428-54554.gif)
A
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034429-90747.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034429-84059.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034429-71536.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034429-90857.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034418-63105.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034418-27407.gif)
⑴已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034418-89826.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034418-16782.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034418-74111.gif)
⑵观察下图:
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034418-38450.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034418-28202.gif)
根据上图,试推测曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034418-69466.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034410-43434.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034411-28162.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034401-34344.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034402-69731.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034401-34344.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026034402-69731.gif)
(1)求动点P的轨迹C的方程;
(2)当t<0时,曲线C的两焦点为F1,F2,若曲线C上存在点Q使得∠F1QF2=120O,
求t的取值范围.
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