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 x2 = 4ay
Since the parabola passes through point (5, 2)
∴ (5)2 = 4a × 2 ⇒ 25 = 8a ⇒ a =

25

8

.
The required equation of parabola is x2 =

4×25

8

y ⇒ x2 =

25

2

y
⇒ 2x2 = 25y