The equation of the directrix of the parabola is x= -6.
Parabola
A parabola is represented algebraically by the standard equation: [tex]4p\left(x-h\right)=\left(y-k\right)^2[/tex], where:
p= focal length
h= x-coordinate of vertex
k= y-coordinate of vertex
The directrix is a line that can be represented by: [tex]directrix: x=h-p[/tex]
The question gives the equation: [tex]\left(y-3\right)^2=20\left(x+1\right)[/tex].
From the comparison between the standard equation of parabola and the given equation, you can see that:
4p=20, then
p=20/4=5
If h=-1 and p=5, you can find the equation of directrix.
[tex]directrix: x=h-p=-1-5\\ \\ directrix:x=-6[/tex]
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