The equation of the parabola is (y-1)^2 = 16(x+3) what is the equation of the directrix of the parabola?

We know that 

if  the y terms is squared so it opens left or right

Is a Horizontal Parabola, the equation is of the form
(y-k)²=4(p)(x-h)
vertex is (h,k)
and
p is distance from focus to vertex, also distance from vertex to directrix
if p>0, then it opens to the right and directrix is to the left of vertex
if p<0, then it opens to the left and directrix is to the right of vertex

so
(y-1)²=4(4)(x-(-3))
vertex is (-3,1)
4>0 so directrix is to left of vertex
left is in x direction
-3-4=-7
directrix is x=-7

the answer is
x=-7

see the attached figure

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