Vertices are (0, ±3) which lie on y-axis.
So the equation of hyperbola in standard form is

y2

a2

−

x2

b2

= 1
Now vertices are (0, ±3) ⇒ a = 3; Co-ordinates of Foci are (0, ±5) ⇒ ae = 5
Now, ae = 5 ⇒ e =

5

a

⇒ e =

5

3

We know that b = a√e2−1 ⇒ b = 3√

25

9

−1 = 3√

16

9

= 4
Thus required equation of hyperbola is

y2

(3)2

−

x2

(4)2

= 1 ⇒

y2

9

−

x2

16

= 1.