What is the directrix (x+5)^2=12(y-2) ?

The directrix (x+5)^2=12(y-2) is y=-1

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

directrix

(x + 5)^{2} = 12 (y - 2)

y = - 1

Solution steps

Rewrite

(x + 5)^{2} = 12 (y - 2)

in the standard form:

4 \cdot 3 (y - 2) = (x - (- 5))^{2}

(h, k) = (- 5, 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

(- 5, 2)

y-coordinate

y = 2 - p

y = 2 - 3

Refine

y = - 1

y^{2} + 4 x - 80 y + 20 = 0

- x^{2} - 4 x + 1

y - 7 = \frac{1}{24} (x + 4)^{2}

4 x^{2} - 24 x - 30

- y^{2} = 6 y + x