题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215112-40820.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215112-70674.png)
(1)设动点P满足PF2-PB2=4,求点P的轨迹;
(2)设x1=2,x2=
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215112-33925.png)
(3)设t=9,求证:直线MN必过x轴上的一定点(其坐标与m无关).
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215112-52351.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215113-18075.png)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215112-52351.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215112-52351.png)
(2)解:将x1=2,x2=
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215112-33925.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215113-92539.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215113-81541.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215114-30272.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215112-33925.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215114-58076.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215114-15740.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215114-31520.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215115-16145.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215113-18075.png)
(3)证明:点T的坐标为(9,m),直线MTA的方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215115-19472.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215115-86725.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215115-72891.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215116-10547.png)
分别与椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215112-40820.png)
M
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215116-98963.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215116-70920.png)
(证法1)当x1≠x2时,直线MN的方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215117-79222.png)
(证法2)若x1=x2,则由
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215117-31291.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215117-98526.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215117-18069.png)
过点D(1,0).若x1≠x2,则m≠2
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215117-98526.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215118-78115.png)
直线ND的斜率kND=
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215118-82833.png)
因此,直线MN必过x轴上的点D(1,0).
核心考点
试题【如图,在平面直角坐标系xOy中,已知椭圆=1的左、右顶点为A、B,右焦点为F.设过点T(t,m)的直线TA、TB与椭圆分别交于点M(x1,y1)、N(x2,y2】;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/20191025/20191025215101-70965.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215102-23323.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215102-82549.png)
(1)求椭圆C的方程;
(2)设G、H为椭圆C上的两个动点,O为坐标原点,且OG⊥OH.
①当直线OG的倾斜角为60°时,求△GOH的面积;
②是否存在以原点O为圆心的定圆,使得该定圆始终与直线GH相切?若存在,请求出该定圆方程;若不存在,请说明理由.
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215046-76154.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215046-77054.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215047-38728.png)
(1)求双曲线C的方程;
(2)求直线AB方程;
(3)如果线段AB的垂直平分线与双曲线交于C、D两点,那么A、B、C、D四点是否共圆?为什么?
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215028-23474.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215028-50349.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215028-41799.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215028-38950.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215007-44235.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215008-28951.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215008-36968.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215008-79199.jpg)
(1)求椭圆C的方程;
(2)求
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215008-30718.png)
(3)设点P是椭圆C上异于M,N的任意一点,且直线MP,NP分别与
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215009-72219.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215009-18136.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215003-13344.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215003-54668.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215003-52785.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215004-55041.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215003-52785.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215004-24256.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025215004-55041.png)
A.圆或椭圆 | B.抛物线或双曲线 | C.椭圆或双曲线 | D.以上均有可能 |
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