What is the directrix y=3x^2 ?

The directrix y=3x^2 is y=-1/12

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directrix y=3x^2

directrix

y = 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}

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

\frac{( x - 1 ) ^{2}}{25} + \frac{( y - 3 ) ^{2}}{16} = 1

6 x^{2} + 12 y - 18 = 0

x^{2} + 8 y + 2 x - 23 = 0

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