Identify the vertex focus and directrix of the graph x^2-8x-28y-124=0

a. vertex (4,5) focus (4,2) directrix y=2.

b. vertex (-4,5) focus (0,7) directrix y=7

c. vertex (4,-5) focus (4,2) directrix y=-12

d. vertex (-4,5) focus (4,-12) directrix y=2

x^2 - 8x - 28y - 124 = 0

Rearranging,

x^2 - 8x = 28y + 124

Using completing the square method on the left hand side:

x^2 - 8x + 16 = 28y + 140

Factoring the left hand and right hand side:

(x - 4) ^2 = 28 (y + 5).

Now just factor out 4 and you have

(x - 4) ² = 4[7 (y + 5) ]

So, Vertex is at (4, - 5)

Focus is at F (4, - 5 + 7) = F (4. 2)

And the directrix is y = - 5 - 7

= - 12.