Answer:
[tex]x=6[/tex]
Step-by-step explanation:
We have been given an equation of a parabola [tex]y^2=-24x[/tex]. We are asked to find the equation of directrix of the given parabola.
First of all, we will convert our given equation in standard form of right-left opening parabola: [tex]4p(x-h)=(y-k)^2[/tex], where, [tex]|p|[/tex] represents focal length and (h,k) is vertex of parabola.
We can rewrite our given equation as:
[tex]-24x=y^2[/tex]
[tex]4(-6)(x-0)=(y-0)^2[/tex]
Since our given parabola has a [tex]y^2[/tex] term, so it will be symmetric about x-axis.
The vertex of parabola is (0,0) and focal length is 6.
We know that equation of directrix of right-left opening parabola is [tex]x=h-p[/tex].
[tex]x=0-(-6)[/tex]
[tex]x=0+6[/tex]
[tex]x=6[/tex]
Therefore, the equation of the directrix of our given parabola is [tex]x=6[/tex].
