What is x^2+y^2-x+6y+1=0 ?

The solution to x^2+y^2-x+6y+1=0 is Circle with (a,b)=(1/2 ,-3),r=(sqrt(33))/2

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x^2+y^2-x+6y+1=0

x^{2} + y^{2} - x + 6 y + 1 = 0

(a, b) = (\frac{1}{2}, - 3), r = \frac{33}{2}

Solution steps

x^{2} + y^{2} - x + 6 y + 1 = 0

Rewrite

x^{2} + y^{2} - x + 6 y + 1 = 0

in the form of the standard circle equation

(x - \frac{1}{2})^{2} + (y - (- 3))^{2} = (\frac{33}{2})^{2}

Therefore the circle properties are:

(a, b) = (\frac{1}{2}, - 3), r = \frac{33}{2}

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

3 x^{2} + 3 y^{2} + 24 x - 12 y = 0

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

x^{2} + y^{2} + 2 x + 6 y = 0

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

What is x^2+y^2-x+6y+1=0 ?
The solution to x^2+y^2-x+6y+1=0 is Circle with (a,b)=(1/2 ,-3),r=(sqrt(33))/2