$\frac{\left|\mathrm{z}-{\mathrm{z}}_1\right|}{\left|\mathrm{z}-{\mathrm{z}}_2\right|}=\mathrm{r}(\mathrm{r}>1)$  represents

$$\begin{gathered} \text{ If }{z}_1\text{ and }{z}_2\text{ are two fixed points, and }k>0,k\ne 1\text{ is a real number, then } \\ \frac{\left|z-z_1\right|}{\left|z-z_2\right|}=k\text{ represents a circle. } \end{gathered}$$

$\mathrm{If} \mathrm{k}>1 \mathrm{then} {\mathrm{z}}_2\mathrm{lies} \mathrm{inside} \mathrm{the} \mathrm{circle} \mathrm{and} {\mathrm{z}}_1\mathrm{lies} \mathrm{out} \mathrm{side} \mathrm{the} \mathrm{circle}$

$\mathrm{If} 0< \mathrm{k}<1 \mathrm{then} {\mathrm{z}}_1\mathrm{lies} \mathrm{inside} \mathrm{the} \mathrm{circle} \mathrm{and} {\mathrm{z}}_2\mathrm{lies} \mathrm{out} \mathrm{side} \mathrm{the} \mathrm{circle}$