What is the directrix x^2-4x+8y-4=0 ?

The directrix x^2-4x+8y-4=0 is y=3

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directrix x^2-4x+8y-4=0

directrix

x^{2} - 4 x + 8 y - 4 = 0

y = 3

Solution steps

Rewrite

x^{2} - 4 x + 8 y - 4 = 0

in the standard form

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

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

(2, 1)

y-coordinate

y = 1 - p

y = 1 - (- 2)

Refine

y = 3

4 t^{2}

3 x^{2} - 2

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

(y + 3)^{2} = 4 (x - 3)

25 x^{2} - 70 x + 36