题目
题型:不详难度:来源:
(Ⅰ)求曲线C1的方程;
(1-4班做)(Ⅱ)设P(x0,y0)(y0≠±3)为圆C2外一点,过P作圆C2的两条切线,分别与曲线C1相交于点A,B和C,D.证明:当P在直线x=﹣4上运动时,四点A,B,C,D的纵坐标之积为定值.
(5-7班做)(Ⅱ)设P(-4,1)为圆C2外一点,过P作圆C2的两条切线,分别与曲线C1相交于点A,B和C,D.证明:四点A,B,C,D的纵坐标之积为定值.
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022152502-30871.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022152503-54523.png)
(Ⅱ)当P在直线
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022152503-88377.png)
解析
(1)由题设知,曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022152502-30871.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022152503-53011.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022152503-39746.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022152504-74202.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022152502-30871.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022152503-39746.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022152504-74202.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022152503-54523.png)
(2)因为P的坐标为
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022152504-54556.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022152503-53011.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022152504-24212.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022152504-49045.png)
设过P所作的两条切线
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022152505-42350.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022152505-48161.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022152505-48161.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022152505-26074.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022152505-43364.png)
(2)当点P在直线
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022152503-88377.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022152506-72998.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022152506-58156.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022152503-53011.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022152504-24212.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022152504-49045.png)
设过P所作的两条切线
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022152505-42350.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022152505-48161.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022152505-48161.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022152505-26074.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022152505-43364.png)
核心考点
试题【在直角坐标系xOy中,曲线C1的点均在C2:(x-5)2+y2=9外,且对C1上任意一点M,M到直线x=﹣2的距离等于该点与圆C2上点的距离的最小值.(Ⅰ)求曲】;主要考察你对直线方程的几种形式等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022152458-85659.png)
A.30º | B. 45º | C.90º | D.135º |
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022152447-18152.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022152448-96246.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022152448-86541.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022152448-94719.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022152448-29097.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022152449-91776.png)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022152449-80278.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022152449-67425.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022152449-38059.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022152449-67425.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022152443-47389.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022152443-44448.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022152444-17278.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022152444-84614.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022152444-86571.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022152443-44448.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022152444-86571.png)
(1)求AB边所在的直线方程;
(2)求中线AM的长
(3)求AB边的高所在直线方程.
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022152436-84866.png)
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