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

The directrix (x-1)^2=-6(y+4) is y=-5/2

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

directrix

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

y = - \frac{5}{2}

Solution steps

Rewrite

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

in the standard form:

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

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

(1, - 4)

y-coordinate

y = - 4 - p

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

Refine

y = - \frac{5}{2}

7 x^{2} + 70 x + 178

x^{2} - 6 x - 28 y = - 93

x^{2} + 17 x + 16

y = (x + 1) (x + 2)

y = x^{2} + x + 1