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

The directrix (x+4)^2=-12(y-2) is y=5

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

directrix

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

y = 5

Solution steps

Rewrite

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

in the standard form:

4 (- 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 = 5

y^{2} - 8 x + 2 y + 25 = 0

(x - 80)^{2} = - 320 (y - 20)

y = x^{2} + 7 x + 5

y = - 10 x^{2}

\frac{1}{8} x^{2} - y = 0