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 \cdot 1 \cdot (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

x^{2} = - 16 y

y - x > - x^{2} - 1

\frac{( y + 1 ) ^{2}}{4} - (x - 5)^{2} = 4

x = \frac{1}{8} y^{2}

x^{2} - 4 y^{2} - 2 x + 16 y = 20