What is the directrix y=(x^2)/(32) ?

The directrix y=(x^2)/(32) is y=-8

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directrix y=(x^2)/(32)

directrix

y = \frac{x ^{2}}{32}

y = - 8

Solution steps

Rewrite

y = \frac{x ^{2}}{32}

in the standard form:

4 \cdot 8 (y - 0) = (x - 0)^{2}

(h, k) = (0, 0), p = 8

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 - 8

Refine

y = - 8

3 y^{2} - 4 x - 6 y + 23 = 0

x^{2} + 4 x - 5

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

x^{2} - x - 56

y^{2} = 4 a x