What is the directrix x^2+12y=0 ?

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directrix x^2+12y=0

directrix

x^{2} + 12 y = 0

y = 3

Solution steps

Rewrite

x^{2} + 12 y = 0

in the standard form:

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

(h, k) = (0, 0), 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

(0, 0)

y-coordinate

y = 0 - p

y = 0 - (- 3)

Refine

y = 3

3 x^{2} - 30 x + 77

y = 2 x^{2} + 28 x + 105

(x - 1)^{2} = - 2 y - 11

(x - 2)^{2} = 8 (y + 1)

y^{2} = 24 x