It is given that, foci (±5,0), the transverse axis is of length 8
Here the foci are on the x-axis.
Therefore, the equation of the hyperbola is of the form x2a2−y2b2=1
Since the foci are (±5,0)⇒ae=c=5
Since the length of the transverse axis is 8, ⇒2a=8⇒a=4
We know that a2+b2=c2
42+b2=52
⇒b2=25−16=9
Thus the equation of the hyperbola is x216−y29=1