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in Parabola by (44.7k points)
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Find the equation of the parabola with vertex at the origin, passing through the point P(5, 2) and symmetric with respect to the y-axis.

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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

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