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

The directrix (y-2)^2=12(x+1) is x=-4

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

directrix

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

x = - 4

Solution steps

Rewrite

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

in the standard form:

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

(h, k) = (- 1, 2), p = 3

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, 2)

x-coordinate

x = - 1 - p

x = - 1 - 3

Refine

x = - 4

y = x^{2} - 5 x - 24

y = - 4 (x + 10)^{2} + 6

y^{2} - 12 y - 4 x + 28 = 0

\frac{6 x}{7} \cdot \frac{4 x}{3}

9 y^{2} - 6 y - 9 - x = 0