What is x^2+6x+9+y^2-2y+1=54+9+1 ?

The solution to x^2+6x+9+y^2-2y+1=54+9+1 is Circle with (a,b)=(-3,1),r=8

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x^2+6x+9+y^2-2y+1=54+9+1

x^{2} + 6 x + 9 + y^{2} - 2 y + 1 = 54 + 9 + 1

(a, b) = (- 3, 1), r = 8

Solution steps

x^{2} + 6 x + 9 + y^{2} - 2 y + 1 = 54 + 9 + 1

Rewrite

x^{2} + 6 x + 9 + y^{2} - 2 y + 1 = 54 + 9 + 1

in the form of the standard circle equation

(x - (- 3))^{2} + (y - 1)^{2} = 8^{2}

Therefore the circle properties are:

(a, b) = (- 3, 1), r = 8

x^{2} = - y^{2} + 10 y + 5

(x - (- 4))^{2} + (y - (2))^{2} = 3^{2}

(x - 12)^{2} + y^{2} = 144

(2 x^{2} + 6 x + 9) + (2 y^{2} + 2 y + 1) = 45 + 9 + 1

4 x^{2} + 4 y^{2} - 16 x - 28 y + 41 = 0

What is x^2+6x+9+y^2-2y+1=54+9+1 ?
The solution to x^2+6x+9+y^2-2y+1=54+9+1 is Circle with (a,b)=(-3,1),r=8