What is the directrix x^2=32y ?

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directrix x^2=32y

directrix

x^{2} = 32 y

y = - 8

Solution steps

Rewrite

x^{2} = 32 y

in the standard form:

4 \cdot 8 (y - 0) = (x - 0)^{2}

(h, k) = (0, 0), p = 8

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 - 8

Refine

y = - 8

y = (x + 6) (x - 2)

6 x^{2} + 7 x - 3

x = - 4 y^{2}

y^{2} - 10 x + 4 y - 16 = 0

- 4 x^{2} + 6 x - 1