What is the directrix y^2-12x-12y+84=0 ?

The directrix y^2-12x-12y+84=0 is x=1

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directrix y^2-12x-12y+84=0

directrix

y^{2} - 12 x - 12 y + 84 = 0

x = 1

Solution steps

Rewrite

y^{2} - 12 x - 12 y + 84 = 0

in the standard form

4 \cdot 3 (x - 4) = (y - 6)^{2}

(h, k) = (4, 6), p = 3

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, 6)

x-coordinate

x = 4 - p

x = 4 - 3

Refine

x = 1

4 x^{2} + 10 x - 10

(x - 7)^{2} = - 12 (y - 1)

y^{2} = 5 y + 7 x + 3

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

- 0.03 x^{2} + 45 x + 124.5