(1)求双曲线9x2-25y2=225的实轴长、虚轴长、焦点坐标、准线方程、渐近线方程、离心率.
(2)设直线y=ax+b与双曲线3x2-y2=1交于A、B，以AB为直径的圆过原点，求点P(a，b)的轨迹方程．
参考答案：
(1)将双曲线方程化为标准方程得
∴a=5，b=3，
∴实轴长2a=10，虚轴长2b=6
焦点坐标
，准线方程
渐近线方程
离心率
(2)联立y=ax+b和双曲线3x2-y2=1，得：
设A、B坐标分别为(x1，y1)、(x2，y2)
则
则
∵O在圆上，AB是直径，∴∠AOB=90°
∴OA· OB=0，即x1x2+y1y2=0
解得：2b2-a2=1
即P的轨迹方程为2y2-x2=1
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