In each of the, 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 vertex is (0, 0) and the axis of the parabola is the x-axis, the equation of the parabola is either of the from y2=4ax or y2 = -4ax.
The parabola passes through point (2, 3), which lies in the first quadrant.
Thus, the equation of the parabola is of the form y2 = 4ax, while point (2, 3) must satisfy the equation y2 = 4ax.
Thus,
32 = 4a(2)
⇒ a = 9/8
Thus, the equation of the parabola is
⇒ 2y2 = 9x
12