Find an equation for the parabola with focus at (2,-8) and vertex at (2,-6)?

Question

[a] x^2 - 4x - 8y - 44 = 0
[b] x^2 + 4x + 8y - 44 = 0
[c] x^2 - 4x +2y +16 = 0
[d] x^2 - 4x + 8y +52 = 0

Answer 1

vertex (h,k)
focus (h,k + p)

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

vertex : (2,-6)
focus : (2,-6 + p)

k + p = -8
-6 + p = -8
p = -2

(x - h)^2 = 4p(y - k)
(x - 2)^2 = 4 * -2(y - (-6))
x^2 - 2x - 2x + 4 = 4 * -2(y + 6)
x^2 - 4x + 4 = -8(y + 6)
x^2 - 4x + 4 = -8y - 48
x^2 - 4x + 8y + 52 = 0

ANS : d.) x^2 - 4x + 8y + 52 = 0

Answer 2

(x-2)^2=-8(y+6)
=>x^2-4x+4=-8y-48
=>x^2-4x+8y+=0
hence (d) is the right answer

Answer 3

c