已知双曲线
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131023211953822930975/SYS201310232119538229309010_ST/0.png)
,P为C上的任意点.
(1)求证:点P到双曲线C的两条渐近线的距离的乘积是一个常数;
(2)设点A的坐标为(3,0),求|PA|的最小值.
考点分析:
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设双曲线
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131023211953822930975/SYS201310232119538229309009_ST/0.png)
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=1的右顶点为A,右焦点为F.过点F平行于双曲线的一条渐近线的直线与双曲线交于点B,则△AFB的面积为
.
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已知双曲线
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131023211953822930975/SYS201310232119538229309008_ST/0.png)
=1的离心率为
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,则n=
.
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已知P是双曲线
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131023211953822930975/SYS201310232119538229309007_ST/0.png)
右支上的一点,双曲线的一条渐近线方程为3x-y=0、设F
1、F
2分别为双曲线的左、右焦点、若|PF
2|=3,则|PF
1|=
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过双曲线
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131023211953822930975/SYS201310232119538229309006_ST/0.png)
的左顶点A作斜率为1的直线l,若l与双曲线M的两条渐近线分别相交于点B,C,且|AB|=|BC|,则双曲线M的离心率是( )
A.
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131023211953822930975/SYS201310232119538229309006_ST/1.png)
B.
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131023211953822930975/SYS201310232119538229309006_ST/2.png)
C.
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131023211953822930975/SYS201310232119538229309006_ST/3.png)
D.
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已知双曲线
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131023211953822930975/SYS201310232119538229309005_ST/0.png)
的一条渐近线方程为
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131023211953822930975/SYS201310232119538229309005_ST/1.png)
,则双曲线的离心率为( )
A.
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131023211953822930975/SYS201310232119538229309005_ST/2.png)
B.
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131023211953822930975/SYS201310232119538229309005_ST/3.png)
C.
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131023211953822930975/SYS201310232119538229309005_ST/4.png)
D.
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