What is the directrix y^2-6y-8x-23=0 ?

The directrix y^2-6y-8x-23=0 is x=-6

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directrix y^2-6y-8x-23=0

directrix

y^{2} - 6 y - 8 x - 23 = 0

x = - 6

Solution steps

Rewrite

y^{2} - 6 y - 8 x - 23 = 0

in the standard form

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

(h, k) = (- 4, 3), 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, 3)

x-coordinate

x = - 4 - p

x = - 4 - 2

Refine

x = - 6

t^{2}

4 x - 3 x^{2}

5 x^{2} + 7

(x + 1)^{2} = - 12 (y - 6)

4 x^{2} - 12 x - 2