Here vertices are (±7, 0) which lie on x-axis.
So, the equation of hyperbola in standard form is

x2

a2

−

y2

b2

= 1.
∴ Vertices are (±7, 0) ⇒ a = 7
Now, e =

4

3

⇒

c

a

=

4

3

⇒

c

7

=

4

3

⇒ c =

28

3

We know that c2 = a2+b2
∴ (

28

3

)2 = (7)2+b2 ⇒ b2 =

784

9

−49 =

343

9

.
Thus required equation of hyperbola is

x2

(7)2

−

y2

343 9

= 1 ⇒

x2

49

−

9y2

343

= 1.