What is the directrix y^2+8x+2y+33=0 ?

The directrix y^2+8x+2y+33=0 is x=-2

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directrix y^2+8x+2y+33=0

directrix

y^{2} + 8 x + 2 y + 33 = 0

x = - 2

Solution steps

Rewrite

y^{2} + 8 x + 2 y + 33 = 0

in the standard form

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

(h, k) = (- 4, - 1), 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

(- 4, - 1)

x-coordinate

x = - 4 - p

x = - 4 - (- 2)

Refine

x = - 2

2 x^{2} - x + 1

y^{2} = x

20 x = y^{2}

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

12 (x - 2) = (y + 2)^{2}