Here foci are (±5, 0) which lie on x-axis.
So the equation of the hyperbola in standard form is

x2

a2

−

y2

b2

= 1.
Now, Foci are (±5, 0) ⇒ ae = 5, Length of transverse axis, 2a = 8 ⇒ a = 4
Now, ae = 5 ⇒ e =

5

a

⇒ e =

5

4

We know that b = a√e2−1 ⇒ b = 4√

25

16

−1 = 4 ×

3

4

= 3
Thus required equation of hyperbola is

x2

(4)2

−

y2

(3)2

= 1 ⇒

x2

16

−

y2

9

= 1.