What is x^2+y^2+x-6y+9=0 ?

The solution to x^2+y^2+x-6y+9=0 is Circle with (a,b)=(-1/2 ,3),r= 1/2

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x^2+y^2+x-6y+9=0

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

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

Solution steps

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

Rewrite

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

in the form of the standard circle equation

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

Therefore the circle properties are:

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

x^{2} + y^{2} - 10 x + 16 y + 85 = 0

16 x^{2} + 16 y^{2} - 8 y - 15 = 0

y^{2} + 2 x + x^{2} = 24 y - 120

(x + 1)^{2} + (y + 2)^{2} = 9

y^{2} = 6 - x^{2}

What is x^2+y^2+x-6y+9=0 ?
The solution to x^2+y^2+x-6y+9=0 is Circle with (a,b)=(-1/2 ,3),r= 1/2