Hi

 Standard Form of an Equation of an Ellipse is where Pt(h,k) is the center 

and a and b  are the respective vertices distances from center.

x^2+4y^2+12x-32y+96=0 

 (x+6)^2 - 36  + 4(y-4)^2 - 4*16  + 96  = 0   

 (x+6)^2 + 4(y-4)^2  = 4

  Center (-6,4) 

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