题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022900-25786.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022900-42394.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022901-42489.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022901-10741.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022901-66721.png)
(Ⅰ)求抛物线
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022901-66721.png)
(Ⅱ)已知直线
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022901-53636.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022902-36789.png)
(ⅰ) 若 |
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022902-31474.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022902-57654.png)
(ⅱ) 过A,B,D分别作y轴的垂线,垂足分别为A1,B1,D1.记
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022902-37654.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022903-55899.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022903-14651.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022903-66847.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022903-84103.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022903-70913.png)
由抛物线定义和已知条件可知
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022904-86282.png)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022904-84051.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022904-48216.png)
(Ⅱ)(ⅰ)解: 设B(x1,y1), D(x2,y2),由
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022904-69723.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022905-50932.png)
由Δ
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022905-19218.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022905-87061.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022905-84658.png)
又由
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022906-17179.png)
故A (4m2,4m).由 | BD |=2 | OA |,得(1+m2)(y1-y2)2=4 (16m4+16m2),
而 (y1-y2)2=16m2+16m,故m=
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022906-28821.png)
(ⅱ) 解: 由(Ⅰ)得x1+x2=m(y1+y2)+2m=4m2+2m.
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022906-54446.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022906-67548.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022906-41104.png)
=
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022907-35428.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022907-37342.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022907-41280.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022905-87061.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022905-84658.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022907-51215.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022908-69737.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022907-51215.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022907-51215.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022903-55899.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022903-55899.png)
所以,
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022903-55899.png)
解析
核心考点
试题【(本题满分15分)已知点在抛物线上,点到抛物线的焦点F的距离为2.(Ⅰ)求抛物线的方程;(Ⅱ)已知直线与抛物线C交于O (坐标原点),A两点,直线与抛物线C交于】;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/20191026/20191026022848-45267.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022849-61312.png)
A.2个 | B.4个 | C.5个 | D.6个 |
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022838-96539.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022838-85392.png)
(1)试
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022838-20288.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022838-92800.png)
(2)若斜率为
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022839-70246.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022839-40762.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022838-92800.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022839-92819.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022839-98607.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022839-33214.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022838-92800.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022840-47003.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022840-97084.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022840-58324.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022840-61907.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022841-43685.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022834-22123.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022834-12494.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022835-45920.png)
A.1 | B.2 | C.3 | D.4 |
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022829-61560.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022829-26453.png)
A.1 | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026022823-32228.png)
(1)求椭圆的标准方程
(2)过椭圆的左焦点F且不与坐标轴垂直的直线交椭圆于A、B两点,线段AB的垂直平分线与x轴交于G点,求G点的横坐标的取值范围
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