What is the directrix (y-2)^2=8(x-1) ?

The directrix (y-2)^2=8(x-1) is x=-1

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directrix (y-2)^2=8(x-1)

directrix

(y - 2)^{2} = 8 (x - 1)

x = - 1

Solution steps

Rewrite

(y - 2)^{2} = 8 (x - 1)

in the standard form:

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

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

Parabola is symmetric around the x-axis and so the directrix is a line parallel to the y-axis, a distance

- p

from the center

(1, 2)

x-coordinate

x = 1 - p

x = 1 - 2

Refine

x = - 1

y = 4 x + 4 x - 2 + x^{2} - 3

y = - 5 x^{2} + 118 x + 7

- x^{2}

x = - 8 y^{2}

y = 4 x^{2} + 23 x - 6