题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004811-48558.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004811-48178.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004811-58830.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004812-80732.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004811-48178.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004812-25383.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004812-76697.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004812-38840.png)
(I)求实数
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004813-90675.png)
(II)当
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004813-99217.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004811-48178.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004813-69626.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004813-81165.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004814-48443.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004811-48178.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004813-81165.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004813-81165.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004813-90675.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004814-64593.png)
(2) 满足题设的点
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004813-81165.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004814-30068.png)
解析
试题分析:解法1:(I)不妨设A
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004814-71213.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004814-50626.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004815-99809.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004812-38840.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004815-15920.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004815-82710.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004816-18770.png)
根据基本不等式
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004816-19924.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004816-34792.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004816-74035.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004817-19997.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004817-20300.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004817-32275.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004813-90675.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004814-64593.png)
(II)当
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004817-73126.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004812-25383.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004812-76697.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004818-31615.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004818-35166.png)
假设抛物线
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004811-48178.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004818-31248.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004819-27158.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004819-73725.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004812-25383.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004812-76697.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004813-81165.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004811-48178.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004813-81165.png)
设经过
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004812-25383.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004812-76697.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004813-81165.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004819-69426.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004819-75988.png)
整理得
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004820-54457.png)
∵函数
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004820-84810.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004820-52686.png)
∴抛物线
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004811-48178.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004818-31248.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004820-83297.png)
∴经过
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004812-25383.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004812-76697.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004813-81165.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004821-75485.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004818-31248.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004820-83297.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004819-27158.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004821-51903.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004821-75485.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004821-52924.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004821-56651.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004821-90347.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004819-27158.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004822-17518.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004822-76719.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004822-61561.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004819-73725.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004822-58144.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004813-81165.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004814-30068.png)
解法2:(I)设
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004812-25383.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004823-76528.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004823-67482.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004815-99809.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004812-38840.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004823-40855.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004823-85298.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004815-82710.png)
显然直线
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004823-85298.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004824-77406.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004823-85298.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004824-65648.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004824-59334.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004824-59334.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004811-58830.png)
得
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004825-87404.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004825-75949.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004817-32275.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004813-90675.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004825-81610.png)
(II)当
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004817-73126.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004812-25383.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004823-76528.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004825-60530.png)
假设抛物线
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004825-97564.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004826-16776.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004819-27158.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004819-73725.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004812-25383.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004823-76528.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004813-81165.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004811-48178.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004813-81165.png)
设圆的圆心坐标为
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004821-75485.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004826-81778.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004826-24723.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004826-80502.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004827-51205.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004827-90712.png)
∵抛物线
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004811-48178.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004813-81165.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004827-34960.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004819-27158.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004821-51903.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004828-36015.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004828-43398.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004828-18258.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004828-11501.png)
代入上式,得
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004828-85302.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004829-61182.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004819-27158.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004819-73725.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004822-58144.png)
故满足题设的点
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004813-81165.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004814-30068.png)
点评:解决该试题的关键是利用抛物线的方程以及性质来分析得到结论,同时对于探索性问题,一般先假设,然后分析求解,属于中档题。
核心考点
试题【(本小题满分12分)已知抛物线:和点,若抛物线上存在不同两点、满足.(I)求实数的取值范围;(II)当时,抛物线上是否存在异于的点,使得经过三点的圆和抛物线在点】;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/20191026/20191026004803-27645.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004803-43193.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004804-42653.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004804-45277.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004804-56956.png)
A.a | B.b | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004753-80450.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004754-66908.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004754-65069.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004754-95999.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004754-60618.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004755-15654.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004755-80422.png)
(Ⅰ)求C1的直角坐标方程;
(Ⅱ)当C1与C2有两个公共点时,求实数
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004755-79262.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004748-68450.jpg)
(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004748-89976.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004749-61506.png)
(4)直线AB与平面BCD成600的角;
其中正确的结论的序号是 。
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004739-34654.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004740-18197.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004740-30232.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004740-56783.png)
(1)求圆
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004739-34654.png)
(2)点
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004741-99355.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004741-19674.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004741-99355.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004739-34654.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004741-62409.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004741-56065.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026004742-41361.png)
A.在同一平面内,动点到两定点的距离之差(大于两定点间的距离)为常数的点的轨迹是双曲线 |
B.在平面内,F1,F2是定点,|F1F2|=6,动点M满足|MF1|+|MF2|=6,则点M的轨迹是椭圆 |
C.“若-3<m<5则方程![]() |
D.在直角坐标平面内,到点![]() ![]() |
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