# Find the equation of the parabola that satisfies the following conditions:

Question:

Find the equation of the parabola that satisfies the following condifions: Focus $(6,0)$; directrix $x=-6$

Solution:

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 $y^{2}=4 a x$ or

$y^{2}=-4 a x$

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 $y^{2}=4 a x$.

Here, $a=6$

Thus, the equation of the parabola is $y^{2}=24 x$.