Question

Find the equation of the parabola with vertex at the origin, axis along X-axis and passing through the point (1, –6)

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 (1, – 6), it lies in 4^th quadrant

∴ Required parabola is y² = 4ax

Substituting x = 1 and y = – 6 in y² = 4ax, we get

(–6)² = 4a(1)

∴ 36 = 4a

∴ a = `36/4` = 9

∴ The required equation of the parabola is

y² = 4(9)x, i.e., y² = 36x.