What is the directrix x^2=40y ?

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directrix x^2=40y

directrix

x^{2} = 40 y

y = - 10

Solution steps

Rewrite

x^{2} = 40 y

in the standard form:

4 \cdot 10 (y - 0) = (x - 0)^{2}

(h, k) = (0, 0), p = 10

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 - 10

Refine

y = - 10

x^{2} - 6 x - y + 33 = 0

- 2 x^{2} + 4 x - 9

y = - \frac{1}{12} x^{2}

\frac{40 x ^{3}}{3 x}

(x - 3)^{2} = - 4 (y + 1)