What is x^2+y^2-1/2 x+1/2 y= 1/8 ?

The solution to x^2+y^2-1/2 x+1/2 y= 1/8 is Circle with (a,b)=(1/4 ,-1/4),r= 1/2

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x^2+y^2-1/2 x+1/2 y= 1/8

x^{2} + y^{2} - \frac{1}{2} x + \frac{1}{2} y = \frac{1}{8}

(a, b) = (\frac{1}{4}, - \frac{1}{4}), r = \frac{1}{2}

Solution steps

x^{2} + y^{2} - \frac{1}{2} x + \frac{1}{2} y = \frac{1}{8}

Rewrite

x^{2} + y^{2} - \frac{1}{2} x + \frac{1}{2} y = \frac{1}{8}

in the form of the standard circle equation

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

Therefore the circle properties are:

(a, b) = (\frac{1}{4}, - \frac{1}{4}), r = \frac{1}{2}

9 x^{2} + 9 y^{2} + 12 x + 36 y - 104 = 0

x^{2} + y^{2} + 4 x = 0

x^{2} + y^{2} + 6 x - 10 y + 18 = 0

4 - x^{2} - y^{2} > 0

x^{2} + y^{2} - 10 x + 9 y + 1 = 0

What is x^2+y^2-1/2 x+1/2 y= 1/8 ?
The solution to x^2+y^2-1/2 x+1/2 y= 1/8 is Circle with (a,b)=(1/4 ,-1/4),r= 1/2