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

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

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

directrix

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

y = - 4

Solution steps

Rewrite

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

in the standard form:

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

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

(4, - 2)

y-coordinate

y = - 2 - p

y = - 2 - 2

Refine

y = - 4

- \frac{1}{8} (y - 8)^{2} + 2

2 x^{2} - 10

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

(y + 1)^{2} = - 4 (x - 2)

(x - h)^{2} = 4 (- 8) (y - 3)