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

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

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

directrix

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

y = - 2

Solution steps

Rewrite

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

in the standard form:

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

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

(2, 1)

y-coordinate

y = 1 - p

y = 1 - 3

Refine

y = - 2

y = x^{2} - 4 x + 9

(3 x - 2) (2 x + 1)

8 - 5 x + x^{2}

x^{2} - 4 x - 5 y + 7 = 0

+ x^{2} + 4 x + 6