What is the directrix y^2=32x ?

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directrix y^2=32x

directrix

y^{2} = 32 x

x = - 8

Solution steps

Rewrite

y^{2} = 32 x

in the standard form:

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

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

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 - 8

Refine

x = - 8

y + 4 x \leq x^{2} + 2

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

9 y^{2} - 16 x^{2} = 81

9 x^{2} - 4 y^{2} - 54 x - 8 y + 113 = 0

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