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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard circle equation

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

Therefore the circle properties are:

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

x^{(2)} - 5 x + y^{(2)} + 4 y = 46

x^{2} + y^{2} + \frac{4}{3} x - \frac{4}{3} y + \frac{4}{9} = 0

3 x^{2} - 9 x + 3 y^{2} + 3 y = \frac{39}{2}

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

x^{2} + y^{2} + 4 x - 8 y + 11 = 0

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