题目内容
(本题12分)△ABC中,∠A=∠B=30°,AB=![](http://thumb.1010pic.com/pic1/imagenew2/czsx/17/86577.png)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/18/86578.png)
【小题1】(1) 当点B在第一象限,纵坐标是
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/19/86579.png)
【小题2】(2) 如果抛物线
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/0/86580.png)
①当
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/1/86581.png)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/2/86582.png)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/3/86583.png)
②设
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/4/86584.png)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/5/86585.png)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/6/86586.png)
【小题1】(1) ∵ 点O是AB的中点, ∴
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/7/86587.png)
设点B的横坐标是x(x>0),则
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/8/86588.png)
解得
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/9/86589.png)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/10/86590.png)
∴ 点B的横坐标是
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/11/86591.png)
【小题2】(2) ① 当
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/12/86592.png)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/13/86593.png)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/14/86594.png)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/15/86595.png)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/16/86596.png)
以下分两种情况讨论.
情况1:设点C在第一象限(如图甲),则点C的横坐标为
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/17/86597.png)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/18/86598.png)
由此,可求得点C的坐标为(
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/17/86597.png)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/0/86600.png)
点A的坐标为(
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/1/86601.png)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/2/86602.png)
∵ A,B两点关于原点对称,
∴ 点B的坐标为 (
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/3/86603.png)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/4/86604.png)
将点A的横坐标代入(*)式右边,计算得
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/2/86602.png)
将点B的横坐标代入(*)式右边,计算得
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/4/86604.png)
∴ 在这种情况下,A,B两点都在抛物线上. (9分)
情况2:设点C在第四象限(如图乙),则点C的坐标为(
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/17/86597.png)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/0/86600.png)
点A的坐标为(
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/3/86603.png)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/2/86602.png)
(
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/1/86601.png)
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/4/86604.png)
经计算,A,B两点都不在这条抛物线上. (10分)
② 存在.m的值是1或-1. (12分)
(
![](http://thumb.1010pic.com/pic1/imagenew2/czsx/13/86613.png)
略
![](http://thumb2018.1010pic.com/images/loading.gif)
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