What is the directrix y=-4x^2 ?

The directrix y=-4x^2 is y= 1/16

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directrix y=-4x^2

directrix

y = - 4 x^{2}

y = \frac{1}{16}

Solution steps

Rewrite

y = - 4 x^{2}

in the standard form:

4 (- \frac{1}{16}) (y - 0) = (x - 0)^{2}

(h, k) = (0, 0), p = - \frac{1}{16}

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}{16})

Refine

y = \frac{1}{16}

\frac{x ^{2}}{25} - \frac{y ^{2}}{9} = 1

x^{2} - 2 x - 4 y + 9 = 0

4 x^{2} + 25 y^{2} = 100

x^{2} = 4 y

x^{2} = - 16 y