由题可设方程为：y^2/a^2-x^2/b^2=1
则：3x-4y=0,y=3x/4=ax/b,a/b=3/4,b=4a/3
5y+3√3=0,y=3√3/5=a^2/c,
a^2+b^2=c^2,a^2+（4a/3）^2=25a^2/9=c^2,a^2=9c^2/25代入y=3√3/5=a^2/c得：
9c/25=3√3/5,c=5√3/3,a=√3,b=4√3/3
则方程为：y^2/3-3x^2/16=1