题目内容
定长为10的线段AB的两端点都在抛物线y2=8x上,则AB中点M的横坐标的最小值为( )A.3
B.4
C.
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182322074777202/SYS201310241823220747772009_ST/0.png)
D.
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182322074777202/SYS201310241823220747772009_ST/1.png)
【答案】分析:
=
=
,由|FA|+|FB|≥|AB|=10,知
.
解答:解:![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182322074777202/SYS201310241823220747772009_DA/4.png)
=![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182322074777202/SYS201310241823220747772009_DA/5.png)
=
,
∵|FA|+|FB|≥|AB|=10,
∴
,
当A,F,B三点共线时,取得最小值.
故选A.
点评:本题考查抛物线的性质和应用,解题时要注意公式的灵活运用.
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182322074777202/SYS201310241823220747772009_DA/0.png)
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182322074777202/SYS201310241823220747772009_DA/1.png)
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182322074777202/SYS201310241823220747772009_DA/2.png)
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182322074777202/SYS201310241823220747772009_DA/3.png)
解答:解:
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182322074777202/SYS201310241823220747772009_DA/4.png)
=
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182322074777202/SYS201310241823220747772009_DA/5.png)
=
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182322074777202/SYS201310241823220747772009_DA/6.png)
∵|FA|+|FB|≥|AB|=10,
∴
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182322074777202/SYS201310241823220747772009_DA/7.png)
当A,F,B三点共线时,取得最小值.
故选A.
点评:本题考查抛物线的性质和应用,解题时要注意公式的灵活运用.
![](http://thumb.zyjl.cn/images/loading.gif)
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定长为10的线段AB的两端点都在抛物线y2=8x上,则AB中点M的横坐标的最小值为( )
A、3 | ||
B、4 | ||
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| ||
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