What is the directrix (x+1)^2=2(y+2) ?

The directrix (x+1)^2=2(y+2) is y=-5/2

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directrix (x+1)^2=2(y+2)

directrix

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

y = - \frac{5}{2}

Solution steps

Rewrite

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

in the standard form:

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

(h, k) = (- 1, - 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

(- 1, - 2)

y-coordinate

y = - 2 - p

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

Refine

y = - \frac{5}{2}

3 x^{2} + 4

3 x^{2} + 2

5 x^{2} + 7 y = 3

x = 4 y^{2} + 12 y + 9

7 x^{2} - 5 x + 9