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

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

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

directrix

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

y = - 3

Solution steps

Rewrite

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

in the standard form:

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

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

(2, - 1)

y-coordinate

y = - 1 - p

y = - 1 - 2

Refine

y = - 3

y^{2} = 24 x

y = - \frac{( x + 3 ) ^{2}}{20} + 1

x^{2} - 6 x + 10

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

y = 2 x^{2} - 3 x