What is the directrix x^2=16y ?

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directrix x^2=16y

directrix

x^{2} = 16 y

y = - 4

Solution steps

Rewrite

x^{2} = 16 y

in the standard form:

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

(h, k) = (0, 0), p = 4

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 - 4

Refine

y = - 4

f (x) = - x^{2} + 6 x + 7

- \frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1

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

- \frac{1}{3} (x - 3) = (y + 5)^{2}

y, x^{2} - y^{2} = 0