Find the equation of the parabola with vertex at the origin, the axis

1.	Find the equation of the parabola with vertex at the origin, the axis along X-axis, and passing through the point: (2, 3)
Answer» 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 y ²= -4ax. Since the parabola passes through (2, 3), it lies in 1st 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 ⇒ y² = 9/2 x ⇒ 2y² = 9x.

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

Answer»

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 y ²= -4ax.

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

⇒ y² = 9/2 x

⇒ 2y² = 9x.