What is the directrix x^2+4x+4y-4=0 ?

The directrix x^2+4x+4y-4=0 is y=3

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directrix x^2+4x+4y-4=0

directrix

x^{2} + 4 x + 4 y - 4 = 0

y = 3

Solution steps

Rewrite

x^{2} + 4 x + 4 y - 4 = 0

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} - 6 y - 8 x + 17 = 0

y^{2} + 6 y + 2 x + 1 = 0

y = x^{2} - 7

2 x - 5 x^{2}

y^{2} - 6 x - 6 y + 3 = 0