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

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

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

center

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

(- 3, 1)

Solution steps

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

Rewrite

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

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

And the center is:

(- 3, 1)

x^{2} + y^{2} + 4 x - 6 y - 12 = 0

x^{2} + y^{2} - 4 x - 8 y + 18 = 0

x^{2} + y^{2} - 10 x + 2 y = 0

(x + 5)^{2} + (y - 2)^{2} = 25

x^{2} + y^{2} + 4 x + 6 y = 23