What is the directrix (x-2)^2=-4(y-2) ?

The directrix (x-2)^2=-4(y-2) is y=3

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directrix (x-2)^2=-4(y-2)

directrix

(x - 2)^{2} = - 4 (y - 2)

y = 3

Solution steps

Rewrite

(x - 2)^{2} = - 4 (y - 2)

in the standard form:

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

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

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, 2)

y-coordinate

y = 2 - p

y = 2 - (- 1)

Refine

y = 3

x - y^{2} = 0

9 x^{2} - 4

- x^{2} + 8 x - 15

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

- 12 y + 10 = x^{2} - 4 x + 14