What is the directrix x^2=6y ?

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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 \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}

x = 3 y^{2}

y = x^{2} + 4 x - 1

y^{2} - 10 y - 12 x + 37 = 0

\frac{x}{25} - y^{2} = 1

y = x^{2} - 10 x - 31