What is the center x^2+y^2-2x-6y-15=0 ?

The center x^2+y^2-2x-6y-15=0 is (1,3)

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center x^2+y^2-2x-6y-15=0

center

x^{2} + y^{2} - 2 x - 6 y - 15 = 0

(1, 3)

Solution steps

x^{2} + y^{2} - 2 x - 6 y - 15 = 0

Rewrite

x^{2} + y^{2} - 2 x - 6 y - 15 = 0

in the form of the standard circle equation

(x - 1)^{2} + (y - 3)^{2} = 5^{2}

Therefore the circle properties are:

(a, b) = (1, 3), r = 5

And the center is:

(1, 3)

x^{2} + 24 x + y^{2} + 10 y = - 160

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

x^{2} + y^{2} + 14 x - 16 y + 64 = 0

2 x^{2} - 2 x + 2 y^{2} + 4 y = - 1

4 x^{2} + 4 y^{2} - 4 x + 2 y + 1 = 0