What is the center x^2+y^2-2x+6y-6=0 ?

The center x^2+y^2-2x+6y-6=0 is (1,-3)

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center x^2+y^2-2x+6y-6=0

center

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

(1, - 3)

Solution steps

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

Rewrite

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

in the form of the standard circle equation

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

Therefore the circle properties are:

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

And the center is:

(1, - 3)

(x - 2)^{2} + (y + 3)^{2} = 36

(x - 3)^{2} + (y + 1)^{2} = 25

x^{2} + y^{2} - 4 x - 2 y - 4 = 0

(x - 1)^{2} + (y + 2)^{2} = 16

x^{2} + y^{2} = 8 (x + y) + 4