Question 657484
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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
{{{(x+2)^2/10 + (y-8)^2/20 = 1}}}
Standard Form of an Equation of an Ellipse is {{{(x-h)^2/a^2 + (y-k)^2/b^2 = 1 }}} 
where Pt(h,k) is the center