What is the directrix y^2=x ?

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directrix y^2=x

directrix

y^{2} = x

x = - \frac{1}{4}

Solution steps

Rewrite

y^{2} = x

in the standard form:

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

(h, k) = (0, 0), p = \frac{1}{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{1}{4}

Refine

x = - \frac{1}{4}

20 x = y^{2}

(x + 5)^{2} = 3 (y - 3)

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

y = - 5 x^{2}

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