Question

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

Answer 1

_Given that _

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

$y^2= 4ax$

or $y^2= - 4ax.$
It is also seen that the directrix, $x= -6$ is to the left of the y-axis, while the focus $(6, 0)$ $$is to the right of the y-axis.
Hence, the parabola is of the form y^2= 4ax. $$$ Here, a = 6$Thus, the equation of the parabola is$y^2= 24x.$ (Ans)