令y^2/16-x^2/9=0.可得题设双曲线方程：y=(±4/3)x.(1)设双曲线方程为x^2/a^2-y^2/b^2=1.由题设可得：9/a^2-12/b^2=1.4a=3b.===>a^2=9/4.b^2=4.故双曲线方程为：x^2/(9/4)-y^2/4=1.(2)设双曲线方程为：y^2/b^2-x^2/a^2=1.4a=3b.===>无实解.综上知,双曲线的方程为：x^2/(9/4)-y^2/4=1.