题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041245-61043.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041245-66046.gif)
(1)设
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041245-51823.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041246-38377.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041246-20253.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041246-75147.gif)
(2)在C1上是否存在点P,使得C1在点P处切线与C2相交于两点A、B,且AB的中垂线恰为C1的切线?若存在,求出点P的坐标;若不存在,说明理由。
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041246-44500.gif)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041246-96168.gif)
设切点分别为
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041247-25209.gif)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041247-88430.gif)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041247-83020.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041247-78863.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041248-94931.gif)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041248-60539.gif)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041248-81379.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041248-56309.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041249-34664.gif)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041249-67022.gif)
则C1在点P处切线方程为:
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041249-83054.gif)
代入
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041249-37586.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041250-69067.gif)
得
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041250-63904.gif)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041250-43968.gif)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041250-84107.gif)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041250-31131.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041251-55713.gif)
由(1)知
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041248-56309.gif)
从而
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041251-79784.gif)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041251-36667.gif)
进而得
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041251-92886.gif)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041252-58110.gif)
所以这样点P存在,其坐标为
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041246-44500.gif)
核心考点
试题【(本小题满分14分)已知抛物线(1)设是C1的任意两条互相垂直的切线,并设,证明:点M的纵坐标为定值;(2)在C1上是否存在点P,使得C1在点P处切线与C2相交】;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,椭圆
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041236-40741.gif)
(Ⅰ)求椭圆C的方程;
(Ⅱ)若AB为垂直于x轴的动弦,直线l:x=4与x轴交于点N,直线AF与BN交于点M.
(ⅰ)求证:点M恒在椭圆C上;
(ⅱ)求△AMN面积的最大值.
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041236-43712.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041222-81494.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041222-50059.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041222-16619.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041223-44670.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041223-55591.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041223-10557.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041223-12422.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041223-99291.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041222-50059.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041223-71443.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041223-41304.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041223-90887.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041223-17602.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041223-99291.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041223-71443.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041223-90887.gif)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041224-53477.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041223-12422.gif)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041224-38719.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041224-40093.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041224-81329.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041212-77700.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041213-42077.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041213-34118.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041207-28916.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041207-72522.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041208-70919.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041208-22906.png)
(1)椭圆的两个焦点坐标分别为(0,2),(0,-2),且点P(
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041202-50455.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041202-14641.gif)
(2)椭圆长轴是
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041202-18058.gif)
(3)双曲线经过点(-3,2),且一条渐近线为y=
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041203-96415.gif)
(4)双曲线离心率为
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041203-73592.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026041203-87037.gif)
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