题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102927-26745.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102927-78780.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102928-68901.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102928-59281.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102928-59281.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102928-63428.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102928-35799.png)
(1)求点P的轨迹C的方程
(2)设A为抛物线
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102928-68901.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102929-85474.png)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102929-36443.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102929-65802.png)
然后根据
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102928-35799.png)
(2)抛物线的准线为x=-2,设A
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102929-34072.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102929-67630.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102930-90515.png)
可得以A为圆心,
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102930-94887.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102930-39858.png)
解:(1)抛物线
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102928-68901.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102929-36443.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102930-81040.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102928-35799.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102931-53331.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102931-21224.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102929-85474.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102931-53331.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102929-85474.png)
(2)抛物线
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102928-68901.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102931-99390.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102929-34072.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102929-67630.png)
⊙C:
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102929-85474.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102931-21719.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102931-53331.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102932-97553.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102930-90515.png)
以A为圆心,
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102930-94887.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102930-39858.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102932-29518.png)
由于BC为两圆公共弦所在直线 由②-①得BC直线方程
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102932-55709.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102930-81040.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102932-14656.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102931-53331.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102932-48563.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102933-98709.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102931-53331.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102933-67714.png)
核心考点
试题【已知⊙O:,为抛物线的焦点,为⊙O外一点,由作⊙O的切线与圆相切于点,且(1)求点P的轨迹C的方程(2)设A为抛物线准线上任意一点,由A向曲线C作两条切线AB、】;主要考察你对抛物线的定义与方程等知识点的理解。[详细]
举一反三
A.圆 | B.椭圆 | C.双曲线 | D.抛物线 |
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102919-13477.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102919-31495.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102919-61170.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102919-84350.png)
A.y2=2x | B.y2=4x |
C.y2=![]() | D.y2=![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102916-79032.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102916-67536.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102917-94168.jpg)
(1)求点P的轨迹T的方程;
(2)试探究在轨迹T上是否存在这样的点:它到直线x=-1的距离恰好等于到点C的距离?若存在,求出这样的点的坐标;若不存在,说明理由.
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102917-41095.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102911-32724.jpg)
(1)求点P的轨迹方程;
(2)求证:△MNP的面积为一个定值,并求出这个定值.
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102908-49867.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102908-22302.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102908-59211.jpg)
(1)求曲线C1和C2的方程;
(2)设点C是C2上一点,若|CF1|=
![](http://img.shitiku.com.cn/uploads/allimg/20191024/20191024102909-85199.png)
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