Here foci are (0, ±13) which lie on y-axis.
So the equation of hyperbola in standard form is

y2

a2

−

x2

b2

= 1.
Now, foci are (0, ±13) ⇒ c = 13
Length of conjugate axis is 2b = 24 ⇒ b = 12
We know that c2 = a2+b2
⇒ (13)2 = a2+(12)2 ⇒ a2 = 169 – 144 = 25
Thus required equation of parabola is

y2

25

−

x2

144

= 1.