What is the directrix x^2+8x-4y-36=0 ?

The directrix x^2+8x-4y-36=0 is y=-14

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directrix x^2+8x-4y-36=0

directrix

x^{2} + 8 x - 4 y - 36 = 0

y = - 14

Solution steps

Rewrite

x^{2} + 8 x - 4 y - 36 = 0

in the standard form

4 \cdot 1 \cdot (y - (- 13)) = (x - (- 4))^{2}

(h, k) = (- 4, - 13), 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

(- 4, - 13)

y-coordinate

y = - 13 - p

y = - 13 - 1

Refine

y = - 14

\frac{1}{400} x^{2} - x + 150

y = (x - 1) (3 x + 1)

y = - x^{2} - 4 x + 6

2 (x - 3)^{2} + 6

y = - 3 x^{2} + 12 x - 8