What is x^2+y^2+x+y-1/2 =0 ?

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

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x^2+y^2+x+y-1/2 =0

x^{2} + y^{2} + x + y - \frac{1}{2} = 0

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

Solution steps

x^{2} + y^{2} + x + y - \frac{1}{2} = 0

Rewrite

x^{2} + y^{2} + x + y - \frac{1}{2} = 0

in the form of the standard circle equation

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

Therefore the circle properties are:

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

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

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

(x - 11)^{2} + (y - 14)^{2} = 8

x^{2} + (y + 2)^{2} = 121

x^{2} + y^{2} - 5 = 0

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