x^2/49+y^2/24=1
则a^2=49,b^2=24,c^2=49-24=25
c=5
焦点坐标是:(-5,0),(5,0)
设双曲线方程是:x^2/a^2-y^2/b^2=1
渐近线方程是:y=(+/-)b/a*x=(+/-)4x/3.
故有:b/a=4/3,4a=3b
又c^2=a^2+b^2
25=a^2+(4a/3)^2
a^2=9
b^2=(4/3)^2a^2=16.
即方程是:x^2/9-y^2/16=1