题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213617-29460.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213617-74029.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213617-14928.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213617-10093.png)
(1)求抛物线的方程,并写出焦点坐标;
(2)是否存在过焦点的直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213617-35837.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213618-12397.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213618-27933.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213618-44772.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213618-24890.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213617-35837.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213618-55380.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213618-71902.png)
解析
试题分析:(1)由抛物线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213617-29460.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213617-74029.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213617-14928.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213617-10093.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213619-84352.png)
(2)由于过焦点的直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213617-35837.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213619-72020.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213619-31423.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213618-24890.png)
解法一:(1)由已知得:
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213619-30285.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213619-81164.png)
焦点坐标为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213620-31680.png)
(2)由题意,设
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213619-72020.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213619-31423.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213619-81164.png)
得到方程:
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213620-67282.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213621-44349.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213621-36747.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213621-71087.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213621-52425.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213621-41107.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213622-52169.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213622-30487.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213622-38723.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213622-30795.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213622-48595.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213622-14078.png)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213622-81458.png)
故直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213617-35837.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213623-64751.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213618-55380.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213618-71902.png)
解法二:(1)(同解法一)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213623-33539.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213623-55488.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213623-69679.png)
不符合题意. 5分
故设
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213619-72020.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213623-33632.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213624-81326.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213619-81164.png)
得到方程:
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213624-72077.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213621-44349.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213621-36747.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213624-51565.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213624-26098.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213625-86968.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213625-96945.png)
点
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213625-88000.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213617-35837.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213626-71320.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213626-68965.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213626-19424.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213626-91606.png)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213627-50130.png)
故直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213617-35837.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213627-41105.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213618-55380.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213618-71902.png)
核心考点
试题【(已知抛物线()的准线与轴交于点.(1)求抛物线的方程,并写出焦点坐标;(2)是否存在过焦点的直线(直线与抛物线交于点,),使得三角形的面积?若存在,请求出直线】;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
A.椭圆、双曲线、圆 |
B.椭圆、双曲线、抛物线 |
C.两条直线、椭圆、圆、双曲线 |
D.两条直线、椭圆、圆、双曲线、抛物线 |
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213602-19690.jpg)
A.[2,+∞) | B.(![]() |
C.![]() | D.(![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213552-26492.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213552-51763.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213552-76575.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213552-22837.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213553-70442.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213553-19367.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213539-91573.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213539-70935.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025213539-12282.png)
(1)求圆C的方程.
(2)试探究圆C上是否存在异于原点的点Q,使Q到椭圆的右焦点F的距离等于线段OF的长,若存在,请求出Q的坐标;若不存在,请说明理由.
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