题目内容
(12分)如图,已知抛物线C:
,
为其准线,过其对称轴上一点P
作直线
与抛物线交于A
、B
两点,连结OA、OB并延长AO、BO分别交
于点M、N。(1)求
的值;
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231155212365356.jpg)
(2)记点Q是点P关于原点的对称点,
设P分有向线段
所成的比为
,
且
求证:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823115520784388.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823115520799184.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823115520846284.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823115520909189.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823115520987402.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823115520987407.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823115521080185.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823115521205499.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231155212365356.jpg)
(2)记点Q是点P关于原点的对称点,
设P分有向线段
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823115521299251.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823115521314197.gif)
且
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823115521314682.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823115521345362.gif)
(1)-1
(1)证明:设
由
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823115521533648.gif)
则![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823115521579794.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823115521611961.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823115521361438.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823115521377603.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823115521533648.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231155215641031.gif)
则
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823115521579794.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823115521595581.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823115521611961.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231155216421431.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231155216731818.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231155216891413.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231155217041428.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231155217201931.gif)
![](http://thumb.zyjl.cn/images/loading.gif)
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