What is x^{(2)}-6x+y^2-2y=6 ?

The solution to x^{(2)}-6x+y^2-2y=6 is Circle with (a,b)=(3,1),r=4

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

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

(a, b) = (3, 1), r = 4

Solution steps

x^{2} - 6 x + y^{2} - 2 y = 6

Rewrite

x^{2} - 6 x + y^{2} - 2 y = 6

in the form of the standard circle equation

(x - 3)^{2} + (y - 1)^{2} = 4^{2}

Therefore the circle properties are:

(a, b) = (3, 1), r = 4

x^{(2)} + (y - 3)^{(2)} = 16

x^{2} + 14 x + 7 + y^{2} + 12 y + 6 = - 21 + 7 + 6

x^{2} + y^{2} + 8 y + 6 = 0

(x + 2)^{2} + (y - 9)^{2} = 144

16 - x^{2} + 2 x - y^{2} - 4 y - 5 > 0

What is x^{(2)}-6x+y^2-2y=6 ?
The solution to x^{(2)}-6x+y^2-2y=6 is Circle with (a,b)=(3,1),r=4