Question

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

Focus (6, 0); directrix x = –6

Answer 1

Focus (6, 0); directrix, x = –6

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

Therefore, the equation of the parabola is either of the form y² = 4ax or

y² = – 4ax.

It is also seen that the directrix, x = –6 is to the left of the y-axis, while the focus (6, 0) is to the right of the y-axis. Hence, the parabola is of the form y² = 4ax.

Here, a = 6

Thus, the equation of the parabola is y² = 24x.