Show that the equation
Question:

Show that the equation $x^{2}+y^{2}-3 x+3 y+10=0$ does not represent a circle.

Solution:

Radius = $\sqrt{g^{2}+f^{2}-c}$

$=\sqrt{\left(-\frac{3}{2}\right)^{2}+\left(-\frac{3^{2}}{2}\right)-10}$

$=\sqrt{\frac{9}{2}-10}=\sqrt{-\frac{11}{2}}$

which implies that the radius is negative. (not possible)

Therefore, $x^{2}+y^{2}-3 x+3 y+10=0$ does not represent a circle.