What is x^2+y^2-x-y=8 ?

The solution to x^2+y^2-x-y=8 is Circle with (a,b)=(1/2 , 1/2),r=sqrt(17/2)

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x^2+y^2-x-y=8

x^{2} + y^{2} - x - y = 8

(a, b) = (\frac{1}{2}, \frac{1}{2}), r = \frac{17}{2}

Solution steps

x^{2} + y^{2} - x - y = 8

Rewrite

x^{2} + y^{2} - x - y = 8

in the form of the standard circle equation

(x - \frac{1}{2})^{2} + (y - \frac{1}{2})^{2} = (\frac{17}{2})^{2}

Therefore the circle properties are:

(a, b) = (\frac{1}{2}, \frac{1}{2}), r = \frac{17}{2}

2 x^{2} + 2 y^{2} + 36 y = - 12 x - 52

x^{2} + y^{2} + 4 x + 18 y - 171 = 0

16 x^{2} + 16 y^{2} + 96 - 40 y - 315 = 0

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

x^{2} + y^{2} + 6 x + 4 y + 12 = 0

What is x^2+y^2-x-y=8 ?
The solution to x^2+y^2-x-y=8 is Circle with (a,b)=(1/2 , 1/2),r=sqrt(17/2)