Equation of circle in general form is given by \[x^{2}+y^{2}+2gx+2fy+c \]
where center is \[(-g , -f) \] and radius is given by \[\sqrt{g^{2}+f^{2}-c} \]
Boundary cases - Since radius must be positive so sum of squares of g and f must be greater than c
\[g^2+f^2 > c \]
For example if equation of cirlce is \[x^2+y^2+8x- 6y+1 \]
center ( -4,3) and radius=\[\sqrt{16+9-1} = \sqrt{16+9-1}=\sqrt{24}=2\sqrt{6} \]
