Question

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

Answer 1

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.