What is the directrix (x+1)^2=-3(y-6) ?

The directrix (x+1)^2=-3(y-6) is y= 27/4

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directrix (x+1)^2=-3(y-6)

directrix

(x + 1)^{2} = - 3 (y - 6)

y = \frac{27}{4}

Solution steps

Rewrite

(x + 1)^{2} = - 3 (y - 6)

in the standard form:

4 (- \frac{3}{4}) (y - 6) = (x - (- 1))^{2}

(h, k) = (- 1, 6), p = - \frac{3}{4}

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, 6)

y-coordinate

y = 6 - p

y = 6 - (- \frac{3}{4})

Refine

y = \frac{27}{4}

- 3 (x - 1)^{2}

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

2 (x^{2} + 6 x) + 5 y + 8 = 0

10 x^{2}

- 4 x^{2} - 2 x + 1

What is the directrix (x+1)^2=-3(y-6) ?
The directrix (x+1)^2=-3(y-6) is y= 27/4