The standard form is

(y-k)² = 4p(x-h)


                0 = y² - 8x + 4y - 20

y² - 8x + 4y - 20 = 0

          y² + 4y = 8x + 20

Multiply the coefficient of y, which is 4, by , getting 2
Then square 2, getting 4, and add 4 to both sides:

      y² + 4y + 4 = 8x + 20 + 4

   (y + 2)(y + 2) = 8x + 24

         (y + 2)² = 4(x + 3)

Compare to the standard form:

         (y - k)² = 4p(x - h)

So the vertex is (h,k) = (-3,-2), 4p = 4, so p = 1

Since p is positive, the parabola opens right.  Since p = 1,

The focus is a point 1 unit to the right of the vertex (-2,-2),
and the directrix is a vertical line 1 unit left of the vertex, 
so its equation is x = -4, the green line:



Edwin