What is x^2-8x+y^2+2y=-16 ?

The solution to x^2-8x+y^2+2y=-16 is Circle with (a,b)=(4,-1),r=1

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

x^{2} - 8 x + y^{2} + 2 y = - 16

(a, b) = (4, - 1), r = 1

Solution steps

x^{2} - 8 x + y^{2} + 2 y = - 16

Rewrite

x^{2} - 8 x + y^{2} + 2 y = - 16

in the form of the standard circle equation

(x - 4)^{2} + (y - (- 1))^{2} = 1^{2}

Therefore the circle properties are:

(a, b) = (4, - 1), r = 1

x^{2} = 12 y

4 x^{2} + y^{2} = 1

16 x^{2} + 9 y^{2} = 144

\frac{x ^{2}}{64} + \frac{y ^{2}}{16} = 1

\frac{y ^{2}}{4} - \frac{x ^{2}}{9} = 1

What is x^2-8x+y^2+2y=-16 ?
The solution to x^2-8x+y^2+2y=-16 is Circle with (a,b)=(4,-1),r=1