What is the directrix x^2+16y=0 ?

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directrix x^2+16y=0

directrix

x^{2} + 16 y = 0

y = 4

Solution steps

Rewrite

x^{2} + 16 y = 0

in the standard form:

4 (- 4) (y - 0) = (x - 0)^{2}

(h, k) = (0, 0), p = - 4

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

(0, 0)

y-coordinate

y = 0 - p

y = 0 - (- 4)

Refine

y = 4

y = 4 x^{2} - 24 x - 30

8 y = x^{2}

x^{2} = 24 (y - 8)

x^{2} = 36 y

(x + 4)^{2} - 1