题目内容
已知椭圆![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133904524227.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231339045551091.gif)
,
得
且
的公共弦
过椭圆
的右焦点。
⑴当
轴时,求
的值,并判断抛物线
的焦点是否在直线
上;
⑵若
,且抛物线
的焦点在直线
上,求
的值及直线AB的方程。
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133904524227.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231339045551091.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133904571142.gif)
得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133904618730.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133904633274.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133904664235.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133904680218.gif)
⑴当
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133904696279.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133904711357.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133904727222.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133904664235.gif)
⑵若
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133904758285.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133904727222.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133904664235.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133904789204.gif)
(1)m=0,p=9/8,
,不在直线
上;
(2)![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231339048361626.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231339048521406.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133904805795.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133904664235.gif)
(2)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231339048361626.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231339048521406.gif)
⑴当
轴时,点![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133904867457.gif)
从而点![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133904898656.gif)
此时,
该焦点不在AB上。
⑵当
,由⑴知:
的斜率存在,设直线
的方程为
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231339050231256.gif)
①
设
则![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133905148619.gif)
因为![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133905164998.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231339051791035.gif)
且![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231339051951109.gif)
从而:![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133905210709.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133904961128.gif)
因为
在直线
上
即
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231339053981621.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133904696279.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133904867457.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133904883609.gif)
从而点
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133904898656.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133904914779.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133904930321.gif)
此时,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133904805795.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133904961128.gif)
⑵当
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133904976673.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133904664235.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133904664235.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231339050231256.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133905039770.gif)
设
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133905054618.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133905148619.gif)
因为
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133905164998.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231339051791035.gif)
且
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231339051951109.gif)
从而:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133905210709.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133904961128.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133905242410.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133905257747.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133905273320.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133905288620.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133905304455.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133905304459.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823133905320671.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231339053981621.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231339054131401.gif)
![](http://thumb.zyjl.cn/images/loading.gif)
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