What is the directrix (x+4)^2=-6(y-3) ?

The directrix (x+4)^2=-6(y-3) is y= 9/2

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directrix (x+4)^2=-6(y-3)

directrix

(x + 4)^{2} = - 6 (y - 3)

y = \frac{9}{2}

Solution steps

Rewrite

(x + 4)^{2} = - 6 (y - 3)

in the standard form:

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

(h, k) = (- 4, 3), p = - \frac{3}{2}

Parabola is symmetric around the y-axis and so the directrix is a line parallel to the x-axis, a distance

- p

from the center

(- 4, 3)

y-coordinate

y = 3 - p

y = 3 - (- \frac{3}{2})

Refine

y = \frac{9}{2}

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

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

(y + 1)^{2} = 2 (x - 5)

- x^{2} + 2 x - 3

y^{2} - 6 x + 6 y + 15 = 0