What is the directrix x^2=-6y ?

The directrix x^2=-6y is y= 3/2

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directrix x^2=-6y

directrix

x^{2} = - 6 y

y = \frac{3}{2}

Solution steps

Rewrite

x^{2} = - 6 y

in the standard form:

4 (- \frac{3}{2}) (y - 0) = (x - 0)^{2}

(h, k) = (0, 0), p = - \frac{3}{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 - (- \frac{3}{2})

Refine

y = \frac{3}{2}

y = - 12 x^{2} + 4 x

x = \frac{1}{12} y^{2}

x = - 4 (y - 7)^{2} + 7

2 y^{2} - 16 x = 0

(x + 2)^{2} - 4