What is x^2+y^2=x+8y ?

The solution to x^2+y^2=x+8y is Circle with (a,b)=(1/2 ,4),r=(sqrt(65))/2

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x^2+y^2=x+8y

x^{2} + y^{2} = x + 8 y

(a, b) = (\frac{1}{2}, 4), r = \frac{65}{2}

Solution steps

x^{2} + y^{2} = x + 8 y

Rewrite

x^{2} + y^{2} = x + 8 y

in the form of the standard circle equation

(x - \frac{1}{2})^{2} + (y - 4)^{2} = (\frac{65}{2})^{2}

Therefore the circle properties are:

(a, b) = (\frac{1}{2}, 4), r = \frac{65}{2}

x^{2} + y^{2} - 12 x + 14 y + 21 = 0

(x - 5)^{2} + (y + 2)^{2} = 121

x^{2} + y^{2} + 5 x + 4 y = 46

9 x^{2} + 9 y^{2} - 6 x + 12 y + 4 = 0

x^{2} + y^{2} + 10 x - 16 y - 55 = 0

What is x^2+y^2=x+8y ?
The solution to x^2+y^2=x+8y is Circle with (a,b)=(1/2 ,4),r=(sqrt(65))/2