Question

Show that the equation x² + y² - 3x + 3y + 10 = 0 does not represent a circle.

Answer 1

Radius = 

\(\sqrt{g^2+f^2-c}\)

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

= \(\sqrt{\frac{9}{2}-10}\) = \(\sqrt{-\frac{11}{2}}\)

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

Therefore, x² + y² - 3x + 3y + 10 = 0 does not represent a circle.