What is the directrix (40x^3)/(3x) ?

The directrix (40x^3)/(3x) is y=-3/160

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directrix (40x^3)/(3x)

directrix

\frac{40 x ^{3}}{3 x}

y = - \frac{3}{160}

Solution steps

Rewrite

y = \frac{40 x ^{3}}{3 x}

in the standard form

4 \cdot \frac{3}{160} (y - 0) = (x - 0)^{2}

(h, k) = (0, 0), p = \frac{3}{160}

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{3}{160}

Refine

y = - \frac{3}{160}

(x - 3)^{2} = - 4 (y + 1)

y = x^{2} - 3 x^{2}

- 2 x^{2} - 4 x + y + 70 = 0

19 - t^{2}

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