题目内容
已知a>0,设F1、F2是双曲线![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182234596783999/SYS201310241822345967839005_ST/0.png)
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182234596783999/SYS201310241822345967839005_ST/1.png)
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182234596783999/SYS201310241822345967839005_ST/2.png)
A.
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182234596783999/SYS201310241822345967839005_ST/3.png)
B.
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182234596783999/SYS201310241822345967839005_ST/4.png)
C.2
D.1
【答案】分析:由
,
,知
=![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182234596783999/SYS201310241822345967839005_DA/3.png)
×
=1=a
=a,由此能得到a的值.
解答:解:∵
,
,
∴
=![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182234596783999/SYS201310241822345967839005_DA/10.png)
×
=1,
∵
=a
=a,
∴a=1.
故选D.
点评:本题考查双曲线的性质和应用,解题时要注意公式的合理选用.
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182234596783999/SYS201310241822345967839005_DA/0.png)
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182234596783999/SYS201310241822345967839005_DA/1.png)
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182234596783999/SYS201310241822345967839005_DA/2.png)
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182234596783999/SYS201310241822345967839005_DA/3.png)
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182234596783999/SYS201310241822345967839005_DA/4.png)
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182234596783999/SYS201310241822345967839005_DA/5.png)
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182234596783999/SYS201310241822345967839005_DA/6.png)
解答:解:∵
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182234596783999/SYS201310241822345967839005_DA/7.png)
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182234596783999/SYS201310241822345967839005_DA/8.png)
∴
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182234596783999/SYS201310241822345967839005_DA/9.png)
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182234596783999/SYS201310241822345967839005_DA/10.png)
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182234596783999/SYS201310241822345967839005_DA/11.png)
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182234596783999/SYS201310241822345967839005_DA/12.png)
∵
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182234596783999/SYS201310241822345967839005_DA/13.png)
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182234596783999/SYS201310241822345967839005_DA/14.png)
∴a=1.
故选D.
点评:本题考查双曲线的性质和应用,解题时要注意公式的合理选用.
![](http://thumb.zyjl.cn/images/loading.gif)
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已知a>0,设F1、F2是双曲线