What is the directrix (y+5)^2=6(x+1) ?

The directrix (y+5)^2=6(x+1) is x=-5/2

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directrix (y+5)^2=6(x+1)

directrix

(y + 5)^{2} = 6 (x + 1)

x = - \frac{5}{2}

Solution steps

Rewrite

(y + 5)^{2} = 6 (x + 1)

in the standard form:

4 \cdot \frac{3}{2} (x - (- 1)) = (y - (- 5))^{2}

(h, k) = (- 1, - 5), p = \frac{3}{2}

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

(- 1, - 5)

x-coordinate

x = - 1 - p

x = - 1 - \frac{3}{2}

Refine

x = - \frac{5}{2}

2 x^{2} + 5

2 y^{2} - 44 x = 0

x = - \frac{3}{8} (y - 2)^{2} - 1

(y + 12)^{2} = 9 (x - 9)

0.5 x^{2} + 2