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

The directrix (x-4)^2=-4(y+2) is y=-1

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

directrix

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

y = - 1

Solution steps

Rewrite

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

in the standard form:

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

(h, k) = (4, - 2), p = - 1

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 - (- 1)

Refine

y = - 1

x = (y + 3)^{2}

13 + 4 x - x^{2}

y = s^{2} + 2 s + 2

(x - 11)^{2}

4 P^{2}