What is the directrix (x+1)^2=12(y-3) ?

The directrix (x+1)^2=12(y-3) is y=0

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directrix (x+1)^2=12(y-3)

directrix

(x + 1)^{2} = 12 (y - 3)

y = 0

Solution steps

Rewrite

(x + 1)^{2} = 12 (y - 3)

in the standard form:

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

(h, k) = (- 1, 3), p = 3

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, 3)

y-coordinate

y = 3 - p

y = 3 - 3

Refine

y = 0

5 x - x^{2}

y^{2} - 12 x - 12 y + 84 = 0

4 x^{2} + 10 x - 10

(x - 7)^{2} = - 12 (y - 1)

y^{2} = 5 y + 7 x + 3