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

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

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

directrix

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

x = - 3

Solution steps

Rewrite

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

in the standard form

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

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

Parabola is symmetric around the x-axis and so the directrix is a line parallel to the y-axis, a distance

- p

from the center

(- 2, - 2)

x-coordinate

x = - 2 - p

x = - 2 - 1

Refine

x = - 3

y = x^{2} - 6 x + 5

2 x^{2} - 19 x + 9

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

x^{2} + 4

x^{2} - 4 x + 5