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

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

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

directrix

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

y = 1

Solution steps

Rewrite

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

in the standard form

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

(h, k) = (- 2, 0), 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, 0)

y-coordinate

y = 0 - p

y = 0 - (- 1)

Refine

y = 1

y = - 2 x^{2}

y = 2 x^{2} - 3

(y + 1)^{2} = 16 (x - 3)

y = + x^{2} - 2 x + 5

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