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

The directrix (x-2)^2=2(y+2) is y=-5/2

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

directrix

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

y = - \frac{5}{2}

Solution steps

Rewrite

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

in the standard form:

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

(h, k) = (2, - 2), p = \frac{1}{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

(2, - 2)

y-coordinate

y = - 2 - p

y = - 2 - \frac{1}{2}

Refine

y = - \frac{5}{2}

x = - \frac{( y + 3 ) ^{2}}{20} + 1

2 x^{2} - 4

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

(y - 6)^{2} = 36 (x - 2)

(x - 0)^{2} = 4 y - 4