What is x^2-2x+1+y^2+y+1/2 = 11/4 ?

The solution to x^2-2x+1+y^2+y+1/2 = 11/4 is Circle with (a,b)=(1,-1/2),r=sqrt(5/2)

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x^2-2x+1+y^2+y+1/2 = 11/4

x^{2} - 2 x + 1 + y^{2} + y + \frac{1}{2} = \frac{11}{4}

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

Solution steps

x^{2} - 2 x + 1 + y^{2} + y + \frac{1}{2} = \frac{11}{4}

Rewrite

x^{2} - 2 x + 1 + y^{2} + y + \frac{1}{2} = \frac{11}{4}

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} + 2 x + y^{2} - 2 y - 45 = 0

4 - (y - 4)^{2} = (x^{2} + 6 x + 9)

z^{2} + y^{2} = 9^{2}

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

3 x^{2} + 3 y^{2} - 12 x - 48 y = 0

What is x^2-2x+1+y^2+y+1/2 = 11/4 ?
The solution to x^2-2x+1+y^2+y+1/2 = 11/4 is Circle with (a,b)=(1,-1/2),r=sqrt(5/2)