Question

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

Focus (0, –3); directrix y = 3

Answer 1

Focus = (0, –3); directrix y = 3

Since the focus lies on the y-axis, the y-axis is the axis of the parabola.

Therefore, the equation of the parabola is either of the form x² = 4ay

x² = – 4ay.

It is also seen that the directrix, y = 3 is above the x-axis, while the focus

(0, –3) is below the x-axis. Hence, the parabola is of the form x² = –4ay.

Here, a = 3

Thus, the equation of the parabola is x² = –12y.