What is the directrix x^2=8y ?

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directrix x^2=8y

directrix

x^{2} = 8 y

y = - 2

Solution steps

Rewrite

x^{2} = 8 y

in the standard form:

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

(h, k) = (0, 0), 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

(0, 0)

y-coordinate

y = 0 - p

y = 0 - 2

Refine

y = - 2

y^{2} = 32 x

16 x^{2} - 9 y^{2} = 144

3 x^{2} + y^{2} + 18 x - 2 y - 8 = 0

x^{2} = 12 y

x^{2} + y^{2} - 6 x + 4 y + 4 = 0