What is the directrix y^2+8x-4y+20=0 ?

The directrix y^2+8x-4y+20=0 is x=0

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directrix y^2+8x-4y+20=0

directrix

y^{2} + 8 x - 4 y + 20 = 0

x = 0

Solution steps

Rewrite

y^{2} + 8 x - 4 y + 20 = 0

in the standard form

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

(h, k) = (- 2, 2), 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

(- 2, 2)

x-coordinate

x = - 2 - p

x = - 2 - (- 2)

Refine

x = 0

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

- 30 x^{2} + 28 x - 6

y^{2} - 20 x = 0

x^{2} = 100 y

x = - \frac{1}{4} (y + 6)^{2} + 7