Vertices are (0, ±5) which lie on y-axis. So the equation of hyperbola in standard form is $\frac{y^2}{a^2} - \frac{x^2}{b^2}$ = 1 Now vertices are (0, ±5) ⇒ a = 5; Foci are (0, ±8) ⇒ ae = 8 Now, ae = 8 ⇒ e = $\frac{8}{a}$ ⇒ e = $\frac{8}{5}$ We know that b = $a\sqrt{e^2-1}$ ⇒ b = $5\sqrt{\frac{64}{25}-1}$ = $\frac{5\sqrt{39}}{5}$ = $\sqrt{39}$ Thus required equation of parabola is $\frac{y^2}{5^2} - \frac{x^2}{(\sqrt{39})^2}$ = 1 ⇒ $\frac{y^2}{25} - \frac{x^2}{39}$ = 1.