若焦点在X轴,
则左右准线方程为x=±a^2/c,
a^2/c-(-a^2/c)=4,
2a^2/c=4,
a^2=2c,
设双曲线方程为：x^2/a^2-y^2/(a^4/4-a^2)=1,
(2√6）^2/a^2-3^2/(a^4/4-a^2)=1,
a^4-28a^2+132=0,
(a^2-22)(a^2-6)=0,
a^2=22,c=11,b^2=c^2-a^2=99,
a^2=6,c=3,b^2=c^2-a^2=3,
∴双曲线方程为：x^2/6-y^2/3=1,
或x^2/22-y^2/99=1.
若焦点在Y轴,
上下准线y=±a^2/c,
c=a^2/2,
没有实数解,
∴双曲线方程为：x^2/6-y^2/3=1,
或x^2/22-y^2/99=1.