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

y2

a2

−

x2

b2

= 1
Now vertices are (0, ±5) ⇒ a = 5; Foci are (0, ±8) ⇒ ae = 8
Now, ae = 8 ⇒ e =

8

a

⇒ e =

8

5

We know that b = a√e2−1 ⇒ b = 5√

64

25

−1 = 5

√39

5

= √39
Thus required equation of parabola is

y2

(5)2

−

x2

(√39)2

= 1 ⇒

y2

25

−

x2

39

= 1.