# Find the equation of the parabola that satisfies the given conditions: Vertex (0,0) passing through (2,3) and axis is along x-axis.

Since the parabola is symmetric about x-axis and has its vertex at the origin, the equation is of the form y2 = 4ax or y2 = -4ax, where the sign depends on whether the parabola opens to the right or left. But the parabola passes through (2, 3) which lies in the first quadrant, it must open to the right. Thus the equation is of the form y2 = 4ax.

Since the parabola passes through (2, 3) we have

32 = 4a(2) ⇒ 9 = 8a ⇒ a = Therefore, the equation of the parabola is

y2 = 4 = x ⇒ 2y2 = 9x.

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