What is the directrix (x-3)^2=4(y+5) ?

The directrix (x-3)^2=4(y+5) is y=-6

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directrix (x-3)^2=4(y+5)

directrix

(x - 3)^{2} = 4 (y + 5)

y = - 6

Solution steps

Rewrite

(x - 3)^{2} = 4 (y + 5)

in the standard form:

4 \cdot 1 \cdot (y - (- 5)) = (x - 3)^{2}

(h, k) = (3, - 5), p = 1

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, - 5)

y-coordinate

y = - 5 - p

y = - 5 - 1

Refine

y = - 6

y = 3 x^{2} + 6 x - 1

9 x^{2} + 24 x + 72 y + 16 = 0

y = x^{2} - 10 x + 5

y = x^{2} - 6 x + 9

x^{2} - 2 x + 8 y + 9 = 0