What is the directrix y^2=8x ?

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directrix y^2=8x

directrix

y^{2} = 8 x

x = - 2

Solution steps

Rewrite

y^{2} = 8 x

in the standard form:

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

(h, k) = (0, 0), p = 2

Parabola is symmetric around the x-axis and so the directrix is a line parallel to the y-axis, a distance

- p

from the center

(0, 0)

x-coordinate

x = 0 - p

x = 0 - 2

Refine

x = - 2

y^{2} = - 8 x

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

9 x^{2} - 36 x - 4 y^{2} - 24 y - 36 = 0

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

4 x^{2} + 3 y^{2} + 8 x - 24 y + 51 = 0