Find the directrix of the parabola with the equation x^{2}+6x+8y+25=0

To find the directrix, convert this equation to standard form by completing the square:

x^{2}+6x+8y+25=0

x^{2}+6x=-8y-25

x^{2}+6x+9=-8y-25+9

(x+3)^{2}=-8y-16

(x+3)^{2}=-8(y+2)

Comparing (x+3)^{2}=-8(y+2) to

(x-h)^{2}=4p(y-k)

k=-2

p=-2

h=-3

The directrix of the parabola is therefore y=k-p=-2-(-2)=0