题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033626-78636.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033626-76041.gif)
(1)求动点
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033626-56244.gif)
(2)设A、B是轨迹
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033626-56244.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033627-70159.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033627-83163.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033627-50353.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033627-44157.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033627-41459.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033627-64311.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033627-58052.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033627-83651.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033628-33762.gif)
答案
(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033628-68748.gif)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033628-50891.gif)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033628-10236.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033628-10236.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033628-87611.gif)
其中
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033628-76657.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033628-27667.gif)
所以轨迹方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033628-68748.gif)
(2)如图,设
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033629-76238.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033629-29608.gif)
(否则
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033629-91149.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033629-68984.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033628-33762.gif)
设其方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033629-30696.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033630-26282.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033629-30696.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033628-68748.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033630-27766.gif)
得
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033630-12007.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033630-39225.gif)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033630-65211.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033631-64159.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033631-18869.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033631-40749.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033631-42796.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033632-84911.gif)
将①式代入上式所以
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033632-86993.gif)
此时,直线
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033628-33762.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033632-12956.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033632-68075.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033632-37347.gif)
所以直线
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033628-33762.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033628-50891.gif)
核心考点
试题【已知动点C到定点的距离比到直线的距离少1,(1)求动点的轨迹的方程;(2)设A、B是轨迹上异于原点的两个不同点,直线和的倾斜角分别为和, 当变化且时,证明直线恒】;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/20191026/20191026033619-48074.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033619-47596.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033620-75697.png)
(Ⅰ)如果k1·k2=,求点A的轨迹方程;
(Ⅱ)如果k1·k2=a,其中a≠0,求点A的轨迹方程,并根据a的取值讨论此轨迹是何种曲线.
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033611-60852.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033611-78083.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033603-51692.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033604-60027.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033604-71133.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033604-28863.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033604-86381.gif)
(1)求轨迹E的方程,并说明该方程所表示曲线的形状;
(2)点
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033605-84801.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033605-82875.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033605-25581.gif)
点
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033605-91700.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033605-83244.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033605-91700.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033600-98612.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033600-17382.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033600-96656.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033600-73781.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033600-96656.gif)
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