What is the directrix (x+6)^2=12(y+1) ?

The directrix (x+6)^2=12(y+1) is y=-4

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directrix (x+6)^2=12(y+1)

directrix

(x + 6)^{2} = 12 (y + 1)

y = - 4

Solution steps

Rewrite

(x + 6)^{2} = 12 (y + 1)

in the standard form:

4 \cdot 3 (y - (- 1)) = (x - (- 6))^{2}

(h, k) = (- 6, - 1), 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

(- 6, - 1)

y-coordinate

y = - 1 - p

y = - 1 - 3

Refine

y = - 4

- \frac{1}{8} (x - 8)^{2} + 2

y = 25 x^{2} - 36

- \frac{1}{2} x^{2} + 7 x - 3

y = - 3 x^{2} + 12 x - 4

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