What is the directrix (y+2)^2=-16(x+9) ?

The directrix (y+2)^2=-16(x+9) is x=-5

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directrix (y+2)^2=-16(x+9)

directrix

(y + 2)^{2} = - 16 (x + 9)

x = - 5

Solution steps

Rewrite

(y + 2)^{2} = - 16 (x + 9)

in the standard form:

4 (- 4) (x - (- 9)) = (y - (- 2))^{2}

(h, k) = (- 9, - 2), p = - 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

(- 9, - 2)

x-coordinate

x = - 9 - p

x = - 9 - (- 4)

Refine

x = - 5

x^{2} + 5 x - 84

2 x^{2} - 32 x - y + 127 = 0

y^{2} + 2 x + 6 y + 17 = 0

(x - 7)^{2}

- 3 x^{2} + 75