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

The directrix (x+2)^2=4(2-y) is y=3

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

directrix

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

y = 3

Solution steps

Rewrite

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

in the standard form:

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

(h, k) = (- 2, 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

(- 2, 2)

y-coordinate

y = 2 - p

y = 2 - (- 1)

Refine

y = 3

y^{2} - 8 x - 4 y - 20 = 0

y = - \frac{1}{2} x^{2} - 2 x + 6

y^{2} - 2 y - 8 x - 39 = 0

(x - 3)^{2} = y - 7

(x - 3)^{2} = 12 (y - 2)