Find the vertex focus and the directrix of the parabola give

Find the vertex, focus and the directrix of the parabola given by y^2 -8y - 8x = - 40. Graph the equation.

y²-8y-8x=-40

we have to use completing the square method here

y²-8y+16 -16-8x=-40

(y-4)²=8x -40 +16

(y-4)²= 8x -24

8x= (y-4)²+24

x=(1/8)(y-4)²+3

comparing it with equation of parabola which is

x= a(y-k)²+h

we get vertex=(3,4)

1/(4p)=1/8

p=2

focus= (h+p,k)=(3+2,4)=(5,4)

directrix , x=h-p

x= 3-2=1

x=1