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

The directrix (x+3)^2=8(y-2) is y=0

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

directrix

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

y = 0

Solution steps

Rewrite

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

in the standard form:

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

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

(- 3, 2)

y-coordinate

y = 2 - p

y = 2 - 2

Refine

y = 0

- 8 x^{2}

y = + (x + 5)^{2} + 3

(y + 6)^{2} = \frac{15}{11} (x + 12)

(y + 6)^{2} = 9 (x - 1)

y^{2} + 10 x = 0