Suppose that $k|z-z_1|=l|z-z_2|$ where $k\neq l$ and both are positive real numbers.
Show that the locus of $z$ in the Argand diagram is a circle with center: $$\frac{k^2 z_1-l^2 z_2}{k^2-l^2}$$ and radius: $$\frac{kl|z_2-z_1|}{|k^2-l^2|}$$ by the Geometric Means method.