What is the directrix (x-1)^2=16(y-2) ?

The directrix (x-1)^2=16(y-2) is y=-2

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directrix (x-1)^2=16(y-2)

directrix

(x - 1)^{2} = 16 (y - 2)

y = - 2

Solution steps

Rewrite

(x - 1)^{2} = 16 (y - 2)

in the standard form:

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

(h, k) = (1, 2), p = 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 - 4

Refine

y = - 2

4 x^{2}

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

y = 3 x^{2} - x + 5

x = y^{2} - y - 42

x^{2} - 4 x - 8 y + 2 = 0