What is the directrix x^2=12y ?

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directrix x^2=12y

directrix

x^{2} = 12 y

y = - 3

Solution steps

Rewrite

x^{2} = 12 y

in the standard form:

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

(h, k) = (0, 0), p = 3

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 - 3

Refine

y = - 3

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

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

\frac{y ^{2}}{9} - \frac{x ^{2}}{4} = 1

x^{2} = 3 y

\frac{a + 1}{b} = \frac{a - 1}{b} + \frac{b + 1}{a}