What is the directrix x^2-6x-12y-51=0 ?

The directrix x^2-6x-12y-51=0 is y=-8

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directrix x^2-6x-12y-51=0

directrix

x^{2} - 6 x - 12 y - 51 = 0

y = - 8

Solution steps

Rewrite

x^{2} - 6 x - 12 y - 51 = 0

in the standard form

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

(h, k) = (3, - 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

(3, - 5)

y-coordinate

y = - 5 - p

y = - 5 - 3

Refine

y = - 8