What is the directrix x=y^2-4 ?

The directrix x=y^2-4 is x=-17/4

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directrix x=y^2-4

directrix

x = y^{2} - 4

x = - \frac{17}{4}

Solution steps

Rewrite

x = y^{2} - 4

in the standard form:

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

(h, k) = (- 4, 0), p = \frac{1}{4}

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

(- 4, 0)

x-coordinate

x = - 4 - p

x = - 4 - \frac{1}{4}

Refine

x = - \frac{17}{4}

y = x^{2} + 5 x - 14

(x + 1)^{2} = - 3 (y - 6)

- 3 (x - 1)^{2}

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

2 (x^{2} + 6 x) + 5 y + 8 = 0