What is the directrix x=-1/4 (y+6)^2+7 ?

The directrix x=-1/4 (y+6)^2+7 is x=8

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directrix x=-1/4 (y+6)^2+7

directrix

x = - \frac{1}{4} (y + 6)^{2} + 7

x = 8

Solution steps

Rewrite

x = - \frac{1}{4} (y + 6)^{2} + 7

in the standard form:

4 (- 1) (x - 7) = (y - (- 6))^{2}

(h, k) = (7, - 6), 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

(7, - 6)

x-coordinate

x = 7 - p

x = 7 - (- 1)

Refine

x = 8

x^{2} + 2 y = 0

y = \frac{4 x ^{3} + 11 x ^{2} + 4 x + 21}{x + 3}

- 2 x^{2} - 12 x - 23

2 x = (y - 3)^{2} + 4

y = \frac{x ^{2}}{28} - \frac{5 x}{14} + \frac{333}{28}