Question

Find the equation of the parabola that satisfies the following condition:

Vertex (0, 0) passing through (2, 3) and axis is along x-axis

Answer 1

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 form y² = 4ax or y² = –4ax.

The parabola passes through point (2, 3), which lies in the first quadrant.

Therefore, the equation of the parabola is of the form y² = 4ax, while point

(2, 3) must satisfy the equation y² = 4ax.

∴ 3² = 4a (2) or a = `9/8`

Thus, the equation of the parabola is

y² = `4(9/8)x`

y² = `9/8x`

2y² = 9x