Since the vertex of the parabola is at (0, 0) and it is symmetrical about the y-axis. ∴ The equation of the parabola is of the form $x^2$ = 4ay Since the parabola passes through point (5, 2) ∴ $(5)^2$ = 4a × 2 ⇒ 25 = 8a ⇒ a = $\frac{25}{8}$. The required equation of parabola is $x^2$ = $\frac{4\times 25}{8} y$ ⇒ $x^2$ = $\frac{25}{2} y$ ⇒ $2x^2$ = 25y