Hi,

-16y+52=-2x^2-8x-y^2

2x^2+8x+y^2-16y = -52

2(x+2)^2 + (y-8)^2 = -52 + 8 + 64

2(x+2)^2 + (y-8)^2 = 20



Standard Form of an Equation of an Ellipse is  

where Pt(h,k) is the center

 

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