What is the directrix 3x^2 ?

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directrix 3x^2

directrix

3 x^{2}

y = - \frac{1}{12}

Solution steps

Rewrite

y = 3 x^{2}

in the standard form:

4 \cdot \frac{1}{12} (y - 0) = (x - 0)^{2}

(h, k) = (0, 0), p = \frac{1}{12}

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{1}{12}

Refine

y = - \frac{1}{12}

y^{2} - 8 x + 2 y + 17 = 0

x^{2} = - 36 y

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

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

\frac{x ^{2}}{16} - \frac{y ^{2}}{36} = 1