Question

Find the equation of the parabola with vertex at the origin, axis along X-axis and passing through the point (2, 3)

Answer 1

Vertex of the parabola is at origin (0, 0) and its axis is along X-axis.

∴ Equation of the parabola can be either y² = 4ax or y² = –4ax.

Since the parabola passes through (2, 3), it lies in 1^st quadrant.

∴ Required parabola is y² = 4ax

Substituting x = 2 and y = 3 in y² = 4ax, we get

(3)² = 4a(2)

∴ 9 = 8a

∴ a = `9/8` 

∴ The required equation of the parabola is

y² = `4(9/8)`x, i.e., y² = `9/2`x, i.e., 2y² = 9x.