Question

Find the equation of the parabola that satisfies the following condition:

Vertex (0, 0) focus (–2, 0)

Answer 1

Vertex (0, 0) focus (–2, 0)

Since the vertex of the parabola is (0, 0) and the focus lies on the negative 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 (–2, 0), a = 2.

Thus, the equation of the parabola is y² = –4(2)x, i.e., y² = –8x