Question

Find the equation of the parabola with vertex at the origin, axis along X-axis and passing through the point (3, 4)

Answer 1

Vertex of the parabola is at the 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 (3, 4), it lies in 1^st quadrant.

∴ Required parabola is y² = 4ax.

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

(4)² = 4a(3)

∴ a = `16/12 = 4/3`

∴ The required equation of the parabola is

y² = `4(4/3)`x, i.e., y² = `(16/3)`x, i.e., 3y² = 16x.