题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021613-30768.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021614-75250.png)
(Ⅰ)求动点Q的轨迹
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021614-69101.png)
(Ⅱ)设点
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021614-73114.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021614-52575.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021614-69101.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021615-80617.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021614-52575.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021615-72359.png)
(Ⅲ)在
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021615-13013.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021615-29769.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021616-44060.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021616-98001.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021614-52575.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021614-69101.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021616-54080.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021615-72359.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021617-22197.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021617-41638.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021617-52430.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021617-41638.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021617-29124.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021618-79800.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021618-44332.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021618-11553.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021618-65318.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021619-97973.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021619-41417.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021619-38603.png)
(3)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021620-86718.png)
解析
试题分析:解:(Ⅰ)设点Q的坐标为(x,y),M(x0,y0),则N(x0,0)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021620-76317.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021613-30768.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021620-21945.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021614-75250.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021620-39025.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021620-16066.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021621-73125.png)
∵点M(x0,y0)在单位圆x2 + y2 = 1上
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021621-21587.png)
所以动点Q的轨迹C的方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021617-29124.png)
(Ⅱ)设
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021621-34512.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021621-93894.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021622-86838.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021622-93613.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021622-67008.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021622-39414.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021618-79800.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021623-74231.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021623-39367.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021618-44332.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021623-42427.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021618-11553.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021623-74231.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021623-94000.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021623-73427.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021618-65318.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021624-40428.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021619-97973.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021623-74231.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021624-48081.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021619-41417.png)
所以,
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021619-38603.png)
(Ⅲ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021615-13013.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021624-85625.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021624-72067.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021625-90512.png)
若正数
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021617-41638.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021625-14749.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021625-51867.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021625-34844.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021626-16302.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021626-17186.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021626-32817.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021626-47720.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021627-45790.png)
所以,当
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021627-19536.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021627-24037.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021627-57736.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021628-48561.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021628-30103.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021617-41638.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021620-86718.png)
点评:解决的关键是利用向量法坐标法得到轨迹方程,同时能利用点到直线的距离得到最值,属于基础题。
核心考点
试题【(本小题满分14分) 已知在单位圆x²+y²=1上任取一点M,作MN⊥x轴,垂足为N, = 2.(Ⅰ)求动点Q的轨迹的方程;(Ⅱ)设点,点为曲线上任一点,求点到】;主要考察你对平面向量应用举例等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021607-48835.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021607-55863.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021608-44257.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021608-72414.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021608-88070.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021608-44257.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021559-59832.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021559-64674.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021559-47127.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021559-94597.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021600-90253.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021552-44881.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021552-44881.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021552-44881.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021552-23572.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021552-23184.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021553-89935.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021542-34693.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021542-12125.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021543-20732.png)
(2)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021543-46353.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021543-15682.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021544-77794.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021520-33237.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021521-22069.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021521-19557.png)
(1)求f(
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105021521-96367.png)
(2)求函数f( x)的单调递增区间.
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