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

The directrix y^2-8y+4x=0 is x=5

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

directrix

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

x = 5

Solution steps

Rewrite

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

in the standard form

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

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

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, 4)

x-coordinate

x = 4 - p

x = 4 - (- 1)

Refine

x = 5

x^{2} + 4 x + 6 y - 2 = 0

48 x - 6 x^{2}

2 x^{2} - x

x^{2} = - 10 y

x^{2} - 4