What is x^2-12x+84=-y^2+16y ?

The solution to x^2-12x+84=-y^2+16y is Circle with (a,b)=(6,8),r=4

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x^2-12x+84=-y^2+16y

x^{2} - 12 x + 84 = - y^{2} + 16 y

(a, b) = (6, 8), r = 4

Solution steps

x^{2} - 12 x + 84 = - y^{2} + 16 y

Rewrite

x^{2} - 12 x + 84 = - y^{2} + 16 y

in the form of the standard circle equation

(x - 6)^{2} + (y - 8)^{2} = 4^{2}

Therefore the circle properties are:

(a, b) = (6, 8), r = 4

x^{2} + y^{2} - 4 x - 8 y - 16 = 0

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

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

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

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

What is x^2-12x+84=-y^2+16y ?
The solution to x^2-12x+84=-y^2+16y is Circle with (a,b)=(6,8),r=4