题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235830-88167.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235831-70263.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235831-70263.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235831-55956.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235831-35431.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235831-56587.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235831-52776.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235831-56587.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235831-52776.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235831-96027.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235832-48550.jpg)
(Ⅰ)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235831-56587.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235831-96027.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235831-52776.png)
(Ⅱ)设直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235832-85356.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235832-98507.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235832-44572.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235832-73740.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235832-94733.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235833-42796.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235833-26075.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235833-13759.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235833-31412.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235834-55523.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235834-75916.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235834-38758.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235834-20636.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235834-15173.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235834-54467.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235830-88167.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235834-84959.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235835-70723.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235835-12051.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235835-69655.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235835-12051.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235835-25329.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235835-34536.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235836-42805.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235836-85839.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235831-56587.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235831-96027.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235831-52776.png)
解析
试题分析:(Ⅰ)由已知,得
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235836-22704.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235832-94733.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235832-94733.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235833-42796.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235833-26075.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235833-13759.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235833-31412.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235836-13068.jpg)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235834-55523.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235834-75916.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235834-38758.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235834-20636.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235834-15173.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235834-54467.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235830-88167.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235834-84959.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235835-70723.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235835-12051.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235835-69655.png)
所以,直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235835-12051.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235836-41795.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235837-48135.png)
所以,直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235835-12051.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235835-25329.png)
同理,直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235835-34536.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235836-42805.png)
②-①并据
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235837-59656.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235836-85839.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235831-56587.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235831-96027.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235831-52776.png)
(Ⅱ)由①②易得y=-1,所以点M的坐标为(2k,-1)(
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235833-26075.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235837-84572.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235838-44163.png)
设C(x3,y3),D(x4,y4), 由
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235838-98206.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235834-75916.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235838-69929.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235838-42671.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235839-42779.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235839-43670.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235839-37404.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235839-75576.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235840-59745.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235840-41164.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235840-96988.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235840-15269.png)
所以,
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235841-17081.png)
当且仅当
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235841-35746.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235832-73740.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235841-25906.png)
点评:当直线与圆锥曲线相交时,常联立方程组转化为关于x的二次方程,进而利用方程的根与系数的关系设而不求的方法化简,在求解时弦长公式
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235841-22254.png)
核心考点
试题【如图,已知抛物线的焦点为,过焦点且不平行于轴的动直线交抛物线于,两点,抛物线在、两点处的切线交于点.(Ⅰ)求证:,,三点的横坐标成等差数列;(Ⅱ)设直线交该抛物】;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/20191025/20191025235823-69134.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235815-18592.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235815-22534.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235815-63153.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235815-41799.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235816-39481.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235816-21394.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235816-49494.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235817-55056.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235817-87404.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235817-41892.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235817-87404.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235817-41892.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235816-21394.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235817-51856.png)
试对双曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235818-69481.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235815-41799.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235816-39481.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235808-92898.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235809-57250.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235809-60349.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235809-93536.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235808-92898.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235809-28976.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235810-43867.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235810-64026.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235810-99498.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235810-94895.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235811-84336.png)
A.45° | B.60° | C.90° | D.120° |
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235759-19663.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235800-30239.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235800-17898.png)
(Ⅱ)动直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235800-33635.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235800-28907.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235800-17898.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235800-23548.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235751-39215.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235751-45537.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235752-63127.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235752-67632.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235752-91794.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025235752-73579.png)
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