What is the directrix y^2-6x-6y+3=0 ?

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

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directrix y^2-6x-6y+3=0

directrix

x = - \frac{5}{2}

Solution steps

Rewrite

y^{2} - 6 x - 6 y + 3 = 0

in the standard form

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

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

(- 1, 3)

x-coordinate

x = - 1 - p

x = - 1 - \frac{3}{2}

Refine

x = - \frac{5}{2}