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

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directrix x^2=-4y

directrix

x^{2} = - 4 y

y = 1

Solution steps

Rewrite

x^{2} = - 4 y

in the standard form:

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

(h, k) = (0, 0), p = - 1

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 - (- 1)

Refine

y = 1

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

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

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

\frac{y ^{2}}{36} - \frac{x ^{2}}{64} = 1

x = y - y^{2}