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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard circle equation

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

Therefore the circle properties are:

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

x^{2} + y^{2} + 5 x - 3 y - 8 = 0

(x + 4)^{2} + (y - 2)^{2} = 9

(x - 11)^{2} + (y + 7)^{2} = 144

x^{2} + y^{2} - 16 x + 12 y + 64 = 0

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

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