Question

Find the equation of the parabola that satisfies the following conditions: Vertex (0, 0); focus (3, 0)

Answer 1

Vertex (0, 0); focus (3, 0)

Since the vertex of the parabola is (0, 0) and the focus lies on the positive x-axis, x-axis is the axis of the parabola, while the equation of the parabola is of the form y² = 4ax.

Since the focus is (3, 0), a = 3.

Thus, the equation of the parabola is y² = 4 × 3 × x, i.e., y² = 12x