What is the directrix (x+4)^2=12y-24 ?

The directrix (x+4)^2=12y-24 is y=-1

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directrix (x+4)^2=12y-24

directrix

(x + 4)^{2} = 12 y - 24

y = - 1

Solution steps

Rewrite

(x + 4)^{2} = 12 y - 24

in the standard form:

4 \cdot 3 (y - 2) = (x - (- 4))^{2}

(h, k) = (- 4, 2), p = 3

Parabola is symmetric around the y-axis and so the directrix is a line parallel to the x-axis, a distance

- p

from the center

(- 4, 2)

y-coordinate

y = 2 - p

y = 2 - 3

Refine

y = - 1

x^{2} - 2 x - 9

y = x^{2} - 8

- 0.4 x^{2} - 5

x + 5 + (y - 3)^{2} = 0

(x + 2)^{2} = 8 (y - 3)