The equation of a parabola with vertex at the origin and symmetric about the y-axis: x2 = 4ay
As we are given, parabola is passing through the point P(5,2).
Putting x = 5 and y = 2 in x2 = 4ay
=> 25 = 4a(2) = 8a
=> a = 25/8
Therefore, equation of parabola:
x2 = 4(25/8 )y = 25/2 y
or 2x2 = 25y