What is the directrix 9x^2 ?

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directrix 9x^2

directrix

9 x^{2}

y = - \frac{1}{36}

Solution steps

Rewrite

y = 9 x^{2}

in the standard form:

4 \cdot \frac{1}{36} (y - 0) = (x - 0)^{2}

(h, k) = (0, 0), p = \frac{1}{36}

Parabola is symmetric around the y-axis and so the directrix is a line parallel to the x-axis, a distance

- p

from the center

(0, 0)

y-coordinate

y = 0 - p

y = 0 - \frac{1}{36}

Refine

y = - \frac{1}{36}

(- x - 1) (x + 3)

+ 12 x^{2} - 14 x

y^{2} = 12 (x - 4)

2 x^{2} - 4 x - 9

y = 4 x^{2} - 2 x + 4