题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014152-43365.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014152-53340.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014152-77286.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014152-77286.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014152-17334.png)
(2)求证:A、F、B三点共线;
(3)求
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014152-66672.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014152-94237.png)
解析
试题分析:(1)准线为y=-1,F(0,1),设P(n,-1),
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014153-76723.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014153-99576.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014153-95628.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014153-93905.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014153-58593.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014154-47976.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014154-24316.png)
所以a,b是方程
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014154-14224.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014154-29916.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014152-17334.png)
(2)由(1)知a+b=2n,
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014155-77199.png)
所以直线AB的方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014155-16960.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014155-20200.png)
因为a+b=2n,ab=-4,所以直线AB的方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014155-95455.png)
所以恒过点F(0,1).
(3)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014155-13608.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014156-19424.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014156-64619.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014156-73179.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014152-66672.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014156-33813.png)
点评:根据导数的几何意义,分别求出切点A,B处的导数即A,B的斜率,然后证明斜率之积为-1,来证明两条切线垂直.证明A,B,F三点共线,关键是利用第(1)问的结果,求出AB的点方程,证明点F的坐标满足此方程即可.第(3)问分别求出
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014156-23982.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014157-89192.png)
核心考点
试题【(12分)已知抛物线的焦点为,准线为,过上一点P作抛物线的两切线,切点分别为A、B,(1)求证:;(2)求证:A、F、B三点共线;(3)求的值.】;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/20191026/20191026014144-18261.png)
A.![]() | B.![]() | C.![]() | D.![]() |
(Ⅰ)函数
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014139-94783.png)
(Ⅱ)若点
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014139-80790.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014139-91122.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014139-60612.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014140-62711.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014140-33797.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014140-50436.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014140-70579.png)
已知
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014130-49072.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014130-22723.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014130-36371.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014130-76498.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014131-87948.png)
(Ⅰ)求椭圆方程;
(Ⅱ)设
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014131-15565.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014131-63152.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014131-99835.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014131-65692.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014132-22667.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014132-69564.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014132-26663.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014132-78704.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014133-10755.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014125-92268.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014125-55895.png)
(1)求抛物线的标准方程;
(2)过点
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014126-81592.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014126-48453.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014126-31487.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014126-85080.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014126-85080.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014115-31851.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014115-10709.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014116-10367.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014116-98975.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014116-52000.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014116-93581.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014116-11635.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014116-52000.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014117-30500.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014116-52000.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014117-38820.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014117-14731.png)
(3)过点
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014117-92775.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014117-84180.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014116-93581.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014117-84180.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014116-52000.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014118-10104.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026014118-21462.png)
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