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A、B、C是我军三个炮兵阵地,A在B的正东方向相距6千米,C在B的北30°西方向,相距4千米,P为敌炮阵地.某时刻,A发现敌炮阵地的某信号,由于B、C比A距P更远,因此,4秒后,B、C才同时发现这一信号(该信号的传播速度为每秒1千米).若从A炮击敌阵地P,求炮击的方位角.

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解:以线段AB的中点为原点,正东方向为x轴的正方向建立直角坐标系,则A(3,0)B(-3,0)C(-5,23)依题意|PB|﹣|PA|=4∴P在以A、B为焦点的双曲线的右支上.这里a=2,c=3,b2=5.其方程为

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