题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181600-11730.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181600-55672.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181600-29771.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181600-91837.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181600-11730.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181600-12118.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181601-39575.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181600-12118.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181601-39575.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181601-80693.gif)
(1)求抛物线的标准方程;
(2)求
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181601-43024.gif)
(3)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181601-79005.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181601-17476.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181601-84780.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181602-32429.gif)
(2)0
(3)证明见解析。
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181602-76567.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181602-20748.gif)
因为点
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181600-29771.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181602-65217.gif)
又点
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181600-29771.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181600-91837.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181602-41838.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181602-30140.gif)
所以抛物线的标准方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181602-32429.gif)
(2)解:点
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181600-11730.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181603-83438.gif)
依题意可知直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181603-28666.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181603-73316.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181603-28666.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181603-30432.gif)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181604-39316.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181604-87770.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181603-28666.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181600-11730.gif)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181604-97305.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181604-75438.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181604-65162.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181604-98775.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181605-76261.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181605-81444.gif)
由于
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181602-32429.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181605-84366.gif)
切线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181605-80572.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181605-83174.gif)
切线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181605-40038.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181605-10343.gif)
由①,②,得
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181605-75011.gif)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181606-42156.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181606-39919.gif)
(3)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181606-55705.gif)
由抛物线的定义知
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181606-75181.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181606-18925.gif)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181606-63181.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181606-59961.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181607-41354.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181607-39748.gif)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181601-79005.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181601-17476.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181601-84780.gif)
核心考点
试题【(本题13分)已知抛物线的焦点在轴上,抛物线上一点到准线的距离是,过点的直线与抛物线交于,两点,过,两点分别作抛物线的切线,这两条切线的交点为.(1)求抛物线的】;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
如图,已知抛物线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181540-22527.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181540-33568.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181540-82094.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181540-33568.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181540-82094.gif)
线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181540-25251.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181540-32438.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181540-49865.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181540-32438.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181540-49865.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181540-33568.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181541-45033.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181541-53550.gif)
(1)求证:直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181541-97391.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181541-93925.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181541-40944.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181541-40944.gif)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181541-72724.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181541-24845.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181541-16671.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181540-82094.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181542-50806.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181534-90515.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181535-79403.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181535-16185.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181535-45817.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181535-36326.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181535-71001.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181535-72689.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181536-84033.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181536-34226.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181528-32466.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181528-70420.gif)
A.
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181528-46524.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181528-74496.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181529-65950.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181529-73088.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181513-35977.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181509-89180.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181509-98230.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181510-26872.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025181510-94183.gif)
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