What is the directrix x=4y^2+12y+9 ?

The directrix x=4y^2+12y+9 is x=-1/16

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directrix x=4y^2+12y+9

directrix

x = - \frac{1}{16}

Solution steps

Rewrite

x = 4 y^{2} + 12 y + 9

in the standard form

4 \cdot \frac{1}{16} (x - 0) = (y - (- \frac{3}{2}))^{2}

(h, k) = (0, - \frac{3}{2}), p = \frac{1}{16}

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

(0, - \frac{3}{2})

x-coordinate

x = 0 - p

x = 0 - \frac{1}{16}

Refine

x = - \frac{1}{16}