What is the directrix y= 1/2 x^2 ?

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

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directrix y= 1/2 x^2

directrix

y = \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}

\frac{y ^{2}}{9} - \frac{x ^{2}}{4} = 1

x^{2} = 3 y

\frac{a + 1}{b} = \frac{a - 1}{b} + \frac{b + 1}{a}

\frac{x ^{2}}{4} + \frac{y ^{2}}{9} = 1

y^{2} - y - x + 1 = 0