What is the center x^2+2x-4y+y^2=76 ?

The center x^2+2x-4y+y^2=76 is (-1,2)

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center x^2+2x-4y+y^2=76

center

x^{2} + 2 x - 4 y + y^{2} = 76

(- 1, 2)

Solution steps

x^{2} + 2 x - 4 y + y^{2} = 76

Rewrite

x^{2} + 2 x - 4 y + y^{2} = 76

in the form of the standard circle equation

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

Therefore the circle properties are:

(a, b) = (- 1, 2), r = 9

And the center is:

(- 1, 2)

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

x^{2} + y^{2} + 6 x - 8 y + 16 = 0

9 x^{2} + 9 y^{2} = 729

x^{2} + y^{2} + 3 x + 4 y + 4 = 0

(x - 9)^{2} + (y + 4)^{2} = 25