Find the equation of the parabola with vertex at the origin, passing through the point P(3, −4) and symmetric about the y-axis.
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),
32=−4×a×(−4) ⇒ a=916.
So, the required equation is
x2=−4×916y ⇒ x2=−94y ⇒ 4x2+9y=0.