Here foci are (±3 √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 (±3 √5,0) ⇒ c = 3√5.
Length of latus rectum is

2b2

a

= 8 ⇒ b2 = 4a
We know that c2 = a2+b2
∴ (3√5)2 = a2 + 4a ⇒ a2 + 4a – 45 = 0
⇒ (a + 9)(a – 5) = 0 ⇒ a = 5 (Since a = –9 is not possible)
∴ a2 = 25 and b2 = 4 × 5 = 20
Thus required equation of hyperbola is

x2

25

−

y2

20

= 1.