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

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

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

directrix

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

y = \frac{5}{2}

Solution steps

Rewrite

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

in the standard form:

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

(h, k) = (- 2, 1), 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

(- 2, 1)

y-coordinate

y = 1 - p

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

Refine

y = \frac{5}{2}

y = - x^{2} + 5 x - 7

- \frac{1}{4} x^{2} + 8 x - 4

y^{2} = 10 x

x^{2} + 1

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