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

The directrix x^2-4x-8y+2=0 is y=-9/4

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

directrix

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

y = - \frac{9}{4}

Solution steps

Rewrite

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

in the standard form

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

(h, k) = (2, - \frac{1}{4}), 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, - \frac{1}{4})

y-coordinate

y = - \frac{1}{4} - p

y = - \frac{1}{4} - 2

Refine

y = - \frac{9}{4}

(3 x - 4) (4 x - 3) - 2 x

(x - 3)^{2} = - 12 y

x^{2} = 10 y

y = 6 x^{2} - 3 x 5

\frac{1}{3} (x + 2)^{2} - 3