What is the directrix x^2=24y ?

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directrix x^2=24y

directrix

x^{2} = 24 y

y = - 6

Solution steps

Rewrite

x^{2} = 24 y

in the standard form:

4 \cdot 6 (y - 0) = (x - 0)^{2}

(h, k) = (0, 0), p = 6

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 - 6

Refine

y = - 6

2 x^{2} + 16 y = 0

x^{2} + y^{2} = 25

9 x^{2} - 54 x + 25 y^{2} - 200 y = - 256

y^{2} = 2 x

y = x^{2} - 24 x - 12