What is the directrix x^2-6y=0 ?

The directrix x^2-6y=0 is y=-3/2

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directrix x^2-6y=0

directrix

x^{2} - 6 y = 0

y = - \frac{3}{2}

Solution steps

Rewrite

x^{2} - 6 y = 0

in the standard form:

4 \cdot \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}

- 8 (y - 3) = (x + 4)^{2}

y = x^{2} - 10 x + 25

y = x^{2} + 10 x - 96

4 (x + 2)^{2} + 5

9 y^{2} + 12 x = 0