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

The solution to x^2+x+y^2+2y=0 is Circle with (a,b)=(-1/2 ,-1),r=(sqrt(5))/2

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

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

(a, b) = (- \frac{1}{2}, - 1), r = \frac{5}{2}

Solution steps

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

Rewrite

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

in the form of the standard circle equation

(x - (- \frac{1}{2}))^{2} + (y - (- 1))^{2} = (\frac{5}{2})^{2}

Therefore the circle properties are:

(a, b) = (- \frac{1}{2}, - 1), r = \frac{5}{2}

(x + 1)^{2} + (y - 3)^{2} = 4

x^{2} + y^{2} - 2 x + 2 y - 7 = 0

x^{2} - 8 x + y^{2} - 6 y + 21 = 0

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

x^{2} + y^{2} - 8 x - 6 y - 24 = 0

What is x^2+x+y^2+2y=0 ?
The solution to x^2+x+y^2+2y=0 is Circle with (a,b)=(-1/2 ,-1),r=(sqrt(5))/2