∵x^2/13+y^2/(13/4)=1.∴a^2-13,b^2=13/4,a>b,焦点在X轴上.
c2=a2-b^2=13-13/4=39/4.
c=±√39/2.
由渐近线 y=±x/2得：b/a=1/2.a=2b
双曲线的焦半径c,c^2==a ^2+b^2=39/4.
(2b)^2+b^2=39/4.
5b^2=39/4,
b^2=39/20.
a^2=(2b)^2=4b^2=39/5
∴所求双曲线方程为：x^2/(39/5-y^2/(39/20)=1.