What is the directrix y=-5x^2 ?

The directrix y=-5x^2 is y= 1/20

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directrix y=-5x^2

directrix

y = - 5 x^{2}

y = \frac{1}{20}

Solution steps

Rewrite

y = - 5 x^{2}

in the standard form:

4 (- \frac{1}{20}) (y - 0) = (x - 0)^{2}

(h, k) = (0, 0), p = - \frac{1}{20}

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}{20})

Refine

y = \frac{1}{20}

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

y = - 3 x^{2} + 17 x - 20

92 x^{2}

y = x^{2} + 6 x + 9

8 (x - 2) = (y + 3)^{2}