What is the directrix x= 1/4 (y+4)^2+2 ?

The directrix x= 1/4 (y+4)^2+2 is x=1

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directrix x= 1/4 (y+4)^2+2

directrix

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

x = 1

Solution steps

Rewrite

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

in the standard form:

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

(h, k) = (2, - 4), p = 1

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

(2, - 4)

x-coordinate

x = 2 - p

x = 2 - 1

Refine

x = 1

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

10 x^{2}

- 4 x^{2} - 2 x + 1

(x + 5)^{2} = 12 (y - 2)

y^{2} + 4 x - 80 y + 20 = 0