What is the directrix y^2=-2x ?

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

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directrix y^2=-2x

directrix

y^{2} = - 2 x

x = \frac{1}{2}

Solution steps

Rewrite

y^{2} = - 2 x

in the standard form:

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

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

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}{2})

Refine

x = \frac{1}{2}

(x - 2)^{2} + (y - 3)^{2} = 64

4 x^{2} - 9 y^{2} = 36

4 x^{2} - 9 y^{2} = 36

f (x) = x^{2} - 8

x^{2} - 24 y + 48 = 0