Compute the foci of the conic section 4x28xy20Solution4 x2 2

Compute the foci of the conic section 4x^2+8x+y^2=0.

4 (x^2 +2x ) +y^2=0
4(x^2 +2x +1) +y^2 =4
4(x+1)^2 +y^2= 4
(x+1)^2 +y^2/4 =1
Ellipse with center at (-1,0) and major axis of 4.
Foci is c^2 = a^2-b^2
c^2 = 4-1=3
c= ±3

Foci are at (-1, 3), (-1,-3)