What is the directrix 1/2 x^2 ?

The directrix 1/2 x^2 is y=-1/2

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directrix 1/2 x^2

directrix

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

y = - \frac{1}{2}

Solution steps

Rewrite

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

in the standard form:

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

(h, k) = (0, 0), p = \frac{1}{2}

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}{2}

Refine

y = - \frac{1}{2}

4 y^{2} - 3 x = 0

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

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

- 30 x^{2} + 28 x - 6

y^{2} - 20 x = 0