What is the foci x^2+4x+4y=-4 ?

The foci x^2+4x+4y=-4 is (-2,-1)

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foci x^2+4x+4y=-4

foci

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

(- 2, - 1)

Solution steps

Rewrite

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

in the standard form

4 (- 1) (y - 0) = (x - (- 2))^{2}

(h, k) = (- 2, 0), p = - 1

Parabola is symmetric around the y-axis and so the focus lies a distance

p

from the center

(- 2, 0)

along the y-axis

(- 2, 0 + p)

= (- 2, 0 + (- 1))

Refine

(- 2, - 1)

6 x^{2} - 24 x - 30

x^{2} + y = 4

y = x^{2} - 4 x - 12

x^{2} = - y

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