What is x^2+12x+y^2-12y=-56 ?

The solution to x^2+12x+y^2-12y=-56 is Circle with (a,b)=(-6,6),r=4

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x^2+12x+y^2-12y=-56

x^{2} + 12 x + y^{2} - 12 y = - 56

(a, b) = (- 6, 6), r = 4

Solution steps

x^{2} + 12 x + y^{2} - 12 y = - 56

Rewrite

x^{2} + 12 x + y^{2} - 12 y = - 56

in the form of the standard circle equation

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

Therefore the circle properties are:

(a, b) = (- 6, 6), r = 4

(x - 1)^{2} + (y + 6)^{2} \leq 4

(x - 10)^{2} + (y + 1)^{2} - 64 = 0

- 3 y^{2} = 3 x^{2} - 2 x - 1

45 = (x - 1)^{2} + (y - (- 3))^{2}

2 x^{2} + 2 y^{2} - 28 x + 12 y + 114 = 0

What is x^2+12x+y^2-12y=-56 ?
The solution to x^2+12x+y^2-12y=-56 is Circle with (a,b)=(-6,6),r=4