渐近线方程为3x=正负2y
可设双曲线的标准方程为:x^2/4p-y^2/9p=1
a^2=4p,b^2=9p
c^2=a^2+b^2=13p
两条准线的距离为16/根号13
2a^2/c=16/√13
8p/√(13p)=16/√13
p=4
双曲线方程为:x^2/16-y^2/36=1
或:设双曲线的标准方程为:-x^2/4p+y^2/9p=1
a^2=9p,b^2=4p
c^2=a^2+b^2=13p
两条准线的距离为16/根号13
2a^2/c=16/√13
18p/√(13p)=16/√13
p=64/81
双曲线方程为:-x^2/4+y^2/9=64/81
所以,双曲线方程为:
x^2/16-y^2/36=1
或,-x^2/4+y^2/9=64/81