What is the directrix x^2-12y-6x+5=0 ?

The directrix x^2-12y-6x+5=0 is y=-10/3

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directrix x^2-12y-6x+5=0

directrix

x^{2} - 12 y - 6 x + 5 = 0

y = - \frac{10}{3}

Solution steps

Rewrite

x^{2} - 12 y - 6 x + 5 = 0

in the standard form

4 \cdot 3 (y - (- \frac{1}{3})) = (x - 3)^{2}

(h, k) = (3, - \frac{1}{3}), p = 3

Parabola is symmetric around the y-axis and so the directrix is a line parallel to the x-axis, a distance

- p

from the center

(3, - \frac{1}{3})

y-coordinate

y = - \frac{1}{3} - p

y = - \frac{1}{3} - 3

Refine

y = - \frac{10}{3}

x^{2} + 4 x - y + 1 = 0

3 x^{2} - 4 x - 2

x^{2} - 5 x - 6

y^{2} + 8 x - 6 y + 25 = 0

5 y = - (x - 3)^{2} - 25