What is the directrix (x-1)^2=4(y-1) ?

The directrix (x-1)^2=4(y-1) is y=0

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directrix (x-1)^2=4(y-1)

directrix

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

y = 0

Solution steps

Rewrite

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

in the standard form:

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

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

(1, 1)

y-coordinate

y = 1 - p

y = 1 - 1

Refine

y = 0

(x - 6)^{2} = 8 (y - 2)

- x^{2} + 6 x + 19

- x^{2} + 5 x + 6

x = - \frac{1}{4} y^{2}

5 x + 3 y^{2} = 0