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 $y^{2}=24 x$.