Posted by pedro on .
Find the vertices and foci of this ellipse 4x^2+16y^2+64x+64y+256=0

algebra 
Steve,
4x^2+16y^2+64x+64y+256=0
4x^2+64x+256 + 16y^2+64y+64 = 256
4(x+8)^2 + 16(y+2)^2 = 256 + 256 + 64
(x+8)^2 + 4(y+2)^2 = 16
(x+8)^2/16 + (y+2)^2/4 = 1
h=8 k=2
a=4 b=2 c=√12
center: (8,2)
vertices: (12,2) (4,2)
foci: (8√12,2) (8+√12,2)