What is (x-3)^2+2y+1-81=-y^2 ?

The solution to (x-3)^2+2y+1-81=-y^2 is Circle with (a,b)=(3,-1),r=9

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(x-3)^2+2y+1-81=-y^2

(x - 3)^{2} + 2 y + 1 - 81 = - y^{2}

(a, b) = (3, - 1), r = 9

Solution steps

(x - 3)^{2} + 2 y + 1 - 81 = - y^{2}

Rewrite

(x - 3)^{2} + 2 y + 1 - 81 = - y^{2}

in the form of the standard circle equation

(x - 3)^{2} + (y - (- 1))^{2} = 9^{2}

Therefore the circle properties are:

(a, b) = (3, - 1), r = 9

(x + 4)^{2} + (y + 2)^{2} = 16

x^{2} + y^{2} - 4 x - 2 y = 11

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

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

2 x^{2} + 2 y^{2} - 16 x + 4 y - 16 = 0

What is (x-3)^2+2y+1-81=-y^2 ?
The solution to (x-3)^2+2y+1-81=-y^2 is Circle with (a,b)=(3,-1),r=9