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

The directrix (x+2)^2=-12(y-5) is y=8

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

directrix

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

y = 8

Solution steps

Rewrite

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

in the standard form:

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

(h, k) = (- 2, 5), 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

(- 2, 5)

y-coordinate

y = 5 - p

y = 5 - (- 3)

Refine

y = 8

y^{2} + 14 y + 4 x + 45 = 0

2 x^{2} + x - 3

y = x^{2} - 8 x + 7

y = \frac{x ( x + 5 )}{7}

x^{2} + 9 x + 20