What is the center x^2+y(y+4)=10x+7 ?

The center x^2+y(y+4)=10x+7 is (5,-2)

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center x^2+y(y+4)=10x+7

center

x^{2} + y (y + 4) = 10 x + 7

(5, - 2)

Solution steps

x^{2} + y (y + 4) = 10 x + 7

Rewrite

x^{2} + y (y + 4) = 10 x + 7

in the form of the standard circle equation

(x - 5)^{2} + (y - (- 2))^{2} = 6^{2}

Therefore the circle properties are:

(a, b) = (5, - 2), r = 6

And the center is:

(5, - 2)

x^{2} + y^{2} - 12 x + 6 y + 36 = 0

9 = 2 y - y^{2} - 6 x - x^{2}

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

(x - 1)^{2} = 27 - (y + 1)^{2}

(x - 5)^{2} + (y - 4)^{2} = 81