What is the directrix x=(y-2)(3y+3) ?

The directrix x=(y-2)(3y+3) is x=-41/6

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directrix x=(y-2)(3y+3)

directrix

x = (y - 2) (3 y + 3)

x = - \frac{41}{6}

Solution steps

Rewrite

x = (y - 2) (3 y + 3)

in the standard form

4 \cdot \frac{1}{12} (x - (- \frac{27}{4})) = (y - \frac{1}{2})^{2}

(h, k) = (- \frac{27}{4}, \frac{1}{2}), p = \frac{1}{12}

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

(- \frac{27}{4}, \frac{1}{2})

x-coordinate

x = - \frac{27}{4} - p

x = - \frac{27}{4} - \frac{1}{12}

Refine

x = - \frac{41}{6}

\frac{1}{4} (x + 2)^{2} - 9

y^{2} - 12 x + 36 = 0

x^{2} - 6 x + 16

x^{2} - 6 x + 18

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