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Question

Find the equation of the parabola with vertex at the origin, passing through the point P(3, 4) and symmetric about the y-axis.


Solution

It is given that the vertex of the parabola is O(0, 0) and it is symmetric about the y-axis.

So, its equation is x2=4ay or x2=4ay.

Since the parabola passes through the point P(3, 4), so it lies in the 4th quadrant.

      it is a downward parabola.

Let its equation be x2=4ay.

Since it passes through the point P(3, 4),

we have 

32=4×a×(4)  a=916.

So, the required equation is 

x2=4×916y  x2=94y  4x2+9y=0.

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