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

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

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

directrix

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

y = - 2

Solution steps

Rewrite

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

in the standard form

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

(h, k) = (- 2, - 1), 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, - 1)

y-coordinate

y = - 1 - p

y = - 1 - 1

Refine

y = - 2

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

- x^{2} + 8 x - 7

y = x^{2} - 5 x + 4

y = x^{2} - x - 6

+ x^{2} + 12