Question 618147
Identify the conic section.  If it is an ellipse or a hyperbola, give the center and foci. 
4x^2+7y^2+32x-56y+148=0
complete the square:
4x^2+32x+7y^2-56y=-148
4(x^2+8x+16)+7(y^2-8y+16)=-148+64+112
4(x+4)^2+7(y-4)^2=28
divide by 28
(x+4)^2/7+(y-4)^2/4=1
This is an equation of an ellipse with horizontal major axis.
equation: (x-h)^2/a^2+(y-k)^2/b^2=1, a>b, (h,k)=(x,y) coordinates of center
For given ellipse:
center: (-4,4)
a^2=7
a=√7≈2.6
b^2=4
b=√4=2
c^2=a^2-b^2=7-4=3
c=√3≈1.7
Foci:(-4±c,4)=(-4±√3,4)=(-4±1.7,4)=(-5.7,4) and (-2.3,4)