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in Parabola by (51.9k 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: 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

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