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 (- 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

16 y^{2} - 32 y - 9 x^{2} - 18 x = 137

4 x^{2} + 4 y^{2} - 4 x + 2 y - 1 = 0

25 x^{2} + 16 y^{2} = 400

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

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