What is the directrix (x-1)^2=8(y+3) ?

The directrix (x-1)^2=8(y+3) is y=-5

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directrix (x-1)^2=8(y+3)

directrix

(x - 1)^{2} = 8 (y + 3)

y = - 5

Solution steps

Rewrite

(x - 1)^{2} = 8 (y + 3)

in the standard form:

4 \cdot 2 (y - (- 3)) = (x - 1)^{2}

(h, k) = (1, - 3), p = 2

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, - 3)

y-coordinate

y = - 3 - p

y = - 3 - 2

Refine

y = - 5

+ 3 x^{2}

(x + 1)^{2} = 12 (y - 3)

5 x - x^{2}

y^{2} - 12 x - 12 y + 84 = 0

4 x^{2} + 10 x - 10