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

The directrix y^2-8x-4y-20=0 is x=-5

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

directrix

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

x = - 5

Solution steps

Rewrite

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

in the standard form

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

(h, k) = (- 3, 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

(- 3, 2)

x-coordinate

x = - 3 - p

x = - 3 - 2

Refine

x = - 5

y = - \frac{1}{2} x^{2} - 2 x + 6

y^{2} - 2 y - 8 x - 39 = 0

(x - 3)^{2} = y - 7

(x - 3)^{2} = 12 (y - 2)

y = 2 x^{2} + 9 x - 3