What is the directrix y^2=3x ?

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directrix y^2=3x

directrix

y^{2} = 3 x

x = - \frac{3}{4}

Solution steps

Rewrite

y^{2} = 3 x

in the standard form:

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

(h, k) = (0, 0), p = \frac{3}{4}

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{3}{4}

Refine

x = - \frac{3}{4}

\frac{x ^{2}}{4} - y^{2} = 1

\frac{x ^{2}}{25} + \frac{y ^{2}}{4} = 1

y = - \frac{x ^{2}}{10} + \frac{9 x}{10} + \frac{11}{5}

2 y^{2} - 12 y - x + 5 = 0

9 x^{2} + 9 y^{2} + 18 x - 18 y + 14 = 0