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

The directrix (x-1)^2=y-2 is y= 7/4

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

directrix

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

y = \frac{7}{4}

Solution steps

Rewrite

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

in the standard form:

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

(h, k) = (1, 2), p = \frac{1}{4}

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, 2)

y-coordinate

y = 2 - p

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

Refine

y = \frac{7}{4}

x^{2} - 4 x + 2

x^{2} - 4 x + 3

y = 3 x - 3 x^{2}

x^{2} - 4 x + 1

y = - x^{2} - 6 x - 13