deriving relation for circle in complex plane Prove that $|z-z_1|²+|z-z_2|²=k$ will represent a circle if $|z_1-z_2|²\leq2k$
I tried using the concept of family of circles, but it didn't help me

Expressing z as $x+yi, z_1=a_1+b_1i, z_2=a_2+b_2i$ so re writing our equation we get $(x-a_1)^2+(y-b_1)^2+(x-a_2)^2+(y-b_2)^2=k$ through simplifying we get that this a circle
