The equation of a parabola with vertex at the origin and symmetric about the y-axis is
x2 = 4ay
Since point P(5,2) passes through above parabola we can write,
52 = 4a(2)
• 25 = 8a
• a = \(\frac{25}{8}\)
Therefore, the equation of a parabola is
• x2 = 4.\(\frac{25}{8}y\)
• x2 = \(\frac{25}{2}y\)
• 2x2 = 25y