The number of values of ' $a$ ' such that the equation $x^2+y^2+4 a x-2 a y+a^2=0$ represents a real

Question

The number of values of ' $a$ ' such that the equation $x^2+y^2+4 a x-2 a y+a^2=0$ represents a real circle is

Professor PC Thomas Classes · Answer

Radius $r = \sqrt{g^2+f^2-c} = \sqrt{4a^2+a^2-a^2} = \sqrt{4a^2} = 2|a| \ge 0$. Real circle for all real $a 
e 0$.