What is x^2+y^2+x+y=0 ?

The solution to x^2+y^2+x+y=0 is Circle with (a,b)=(-1/2 ,-1/2),r=sqrt(1/2)

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x^2+y^2+x+y=0

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

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

Solution steps

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

Rewrite

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

in the form of the standard circle equation

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

Therefore the circle properties are:

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

x^{2} + y^{2} - 8 x + 4 y - 29 = 0

x^{2} + y^{2} - 2 x - 8 y + 13 = 0

x^{2} + y^{2} + 16 x - 16 y + 79 = 0

x^{2} + y^{2} - 10 x + 4 y + 4 = 0

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

What is x^2+y^2+x+y=0 ?
The solution to x^2+y^2+x+y=0 is Circle with (a,b)=(-1/2 ,-1/2),r=sqrt(1/2)