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} + 4 x + 2 y - 4 = 0

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

x^{2} + y^{2} - 12 x + 35 = 0

x^{2} - 12 x + 84 = - y^{2} + 16 y

x^{2} + y^{2} - 4 x - 8 y - 16 = 0

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