What is the directrix y^2+4x-80y+20=0 ?

The directrix y^2+4x-80y+20=0 is x=396

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directrix y^2+4x-80y+20=0

directrix

y^{2} + 4 x - 80 y + 20 = 0

x = 396

Solution steps

Rewrite

y^{2} + 4 x - 80 y + 20 = 0

in the standard form

4 (- 1) (x - 395) = (y - 40)^{2}

(h, k) = (395, 40), 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

(395, 40)

x-coordinate

x = 395 - p

x = 395 - (- 1)

Refine

x = 396

- x^{2} - 4 x + 1

y - 7 = \frac{1}{24} (x + 4)^{2}

4 x^{2} - 24 x - 30

- y^{2} = 6 y + x

x = - \frac{1}{20} (y + 6)^{2} - 7