题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033519-35708.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033520-50915.gif)
(1)求P点的轨迹方程并讨论轨迹是什么曲线?
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033520-81017.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033520-10573.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033520-38865.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033521-79288.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033521-30625.gif)
(3)在(2)的条件下,设
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033521-75667.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033521-91627.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033520-38865.gif)
答案
(1)略
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033521-45604.gif)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033522-92372.jpg)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033520-81017.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033522-88214.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033520-38865.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033522-67985.gif)
与曲线C方
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033522-29507.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033523-71062.gif)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033523-37060.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033523-99652.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033523-38108.gif)
可得
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033523-35298.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033524-81162.gif)
(3)由
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033524-82708.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033524-85281.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033524-66668.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033525-80432.gif)
③式平方除以④式得:
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033525-31133.gif)
而
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033525-57657.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033521-91627.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033525-42302.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033525-14520.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033520-38865.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033526-97405.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033526-25255.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033521-45604.gif)
核心考点
试题【 已知M(-3,0)﹑N(3,0),P为坐标平面上的动点,且直线PM与直线PN的斜率之积为常数m(m-1,m0).(1)求P点的轨迹方程并讨论轨迹是什么曲线?(】;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
如图,已知
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033503-20033.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033503-76594.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033503-31245.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033503-31245.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033504-21791.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033504-34687.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033504-74347.gif)
(Ⅰ)求动点
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033503-31245.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033504-52572.gif)
(Ⅱ)过点
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033505-26837.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033504-52572.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033505-18786.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033505-93554.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033504-21791.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033505-56014.gif)
(1)已知
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033506-42070.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033506-19736.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033506-27322.gif)
(2)求
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033506-88377.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033457-88113.gif)
垂直x轴于D,动点Q满足
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033458-46500.gif)
(1)求动点Q的轨迹方程;
(2)已知点E(1,1),在动点Q的轨迹上是
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033458-65166.gif)
使
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033458-68840.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033458-33746.gif)
若不存在,请说明理由。
①
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033453-58370.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033454-75097.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033454-14830.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033454-93968.png)
其中与直线
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033454-26292.png)
A.①③ | B.②④ | C.①②③ | D.②③④ |
设
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033442-12990.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033442-88066.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033442-98639.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033442-67637.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033443-31369.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033443-82750.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033443-58784.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033443-25081.gif)
(Ⅰ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033443-31369.gif)
(Ⅱ)设点
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033444-33914.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033444-50219.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033443-31369.gif)
在直角坐标系
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033433-57564.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033433-68218.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033434-11174.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033434-18491.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033434-20872.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033434-42480.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033434-20872.gif)
(Ⅰ)求曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033434-20872.gif)
(Ⅱ)若以线段AB为直径的圆过坐标原点,求
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033434-64555.gif)
(Ⅲ)当实数
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033434-64555.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026033435-74926.gif)
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