What is the directrix (x-6)^2=8(y+4) ?

The directrix (x-6)^2=8(y+4) is y=-6

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directrix (x-6)^2=8(y+4)

directrix

(x - 6)^{2} = 8 (y + 4)

y = - 6

Solution steps

Rewrite

(x - 6)^{2} = 8 (y + 4)

in the standard form:

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

(h, k) = (6, - 4), p = 2

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, - 4)

y-coordinate

y = - 4 - p

y = - 4 - 2

Refine

y = - 6

y = - 3 x^{2} - 42 x - 22

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

x^{2} - 2 x - 24

18 x^{2} - 64 x - 14 y + 150 = 0

2 x^{2} + 5 x