Vertices are (±2, 0) which lie on x-axis.
So the equation of hyperbola in standard form is

x2

a

−

y2

b2

= 1
∴ Vertices are (±2, 0) ⇒ a = 2; Foci are (±3, 0) ⇒ ae = 3
Now, ae = 3 ⇒ e =

3

a

⇒ e =

3

2

We know that b = a√e2−1 ⇒ b = 2√

9

4

−1 = 2

√5

2

= √5
Thus required equation of hyperbola is

x2

(2)2

−

y2

(√5)2

= 1 ⇒ x2−4

y2

5

= 1