The equation $\left|z - i\right| + \left|z + i\right| = k, k >0$, can represent an ellipse if ${\mathrm{k}}^2$ is

$|\mathrm{z}+\mathrm{i}|+|\mathrm{z}-\mathrm{i}|=\mathrm{k},\mathrm{ }\mathrm{k}>0$ represents an ellipse with foci at   $S\left(\mathrm{0,1}\right)\mathrm{ }\mathrm{S}\text{'}(0,-1)$ and   length of major axis = k.

$SS\text{'} <\hspace{0.17em}\mathrm{k}$ or $\mathrm{k} >\hspace{0.17em}SS\text{'}$

$$\begin{gathered} \mathrm{k} > 2 \\ \therefore {\mathrm{k}}^2 >\hspace{0.17em}4 \end{gathered}$$