Find the equation of the parabola with vertex at the origin, passing t

1.	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.
Answer» 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

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.

Answer»

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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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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