What is x^2+y^2-x-2y+1/4 =0 ?

The solution to x^2+y^2-x-2y+1/4 =0 is Circle with (a,b)=(1/2 ,1),r=1

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x^2+y^2-x-2y+1/4 =0

x^{2} + y^{2} - x - 2 y + \frac{1}{4} = 0

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

Solution steps

x^{2} + y^{2} - x - 2 y + \frac{1}{4} = 0

Rewrite

x^{2} + y^{2} - x - 2 y + \frac{1}{4} = 0

in the form of the standard circle equation

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

Therefore the circle properties are:

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

1000 = 200 (1 + x^{2} + y^{2})

x^{2} + y^{2} + 12 x - 16 y - 1 = 0

x^{2} + y^{2} + 2 x + 2 y + 8 - 36 = 0

x^{2} + y^{2} + 4 x - 6 y - 36 = 0

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

What is x^2+y^2-x-2y+1/4 =0 ?
The solution to x^2+y^2-x-2y+1/4 =0 is Circle with (a,b)=(1/2 ,1),r=1