What is the directrix 9y^2+12x=0 ?

The directrix 9y^2+12x=0 is x= 1/3

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directrix 9y^2+12x=0

directrix

9 y^{2} + 12 x = 0

x = \frac{1}{3}

Solution steps

Rewrite

9 y^{2} + 12 x = 0

in the standard form:

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

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

(0, 0)

x-coordinate

x = 0 - p

x = 0 - (- \frac{1}{3})

Refine

x = \frac{1}{3}

2 y^{2} - 16 y + 72 = 20 x

\frac{1}{2} x^{2}

4 y^{2} - 3 x = 0

y^{2} + 8 x - 4 y + 20 = 0

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