If the equation ${\left|\mathrm{z} - {\mathrm{z}}_1\right|}^2 + {\left|\mathrm{z} - {\mathrm{z}}_2\right|}^2 = \mathrm{k}$ represent the equation of a circle, where $z_1 = 2 + 3i, z_2 = 4 + 3i$ are the extremities of a diameter, then the value of k is

${\left|\mathrm{z}-{\mathrm{z}}_1\right|}^2+{\left|\mathrm{z}-{\mathrm{z}}_2\right|}^2=\mathrm{k}$

Let $\mathrm{A}={\mathrm{z}}_1=2+3\mathrm{i}, \mathrm{B}={\mathrm{z}}_2=4+3\mathrm{i}$  lies on the circle A, B , are extremities of a diameter P(z) lies on the circle

$$\begin{gathered} \Rightarrow \mathrm{ }{\mathrm{PA}}^2+{\mathrm{PB}}^2={\mathrm{AB}}^2 \\ |\mathrm{z}-{\mathrm{z}}_1{|}^2+|\mathrm{z}-{\mathrm{z}}_2{|}^2=|{\mathrm{z}}_1-{\mathrm{z}}_2{|}^2 \\ \therefore \mathrm{K}=|2+3\mathrm{i}-4-3\mathrm{i}{|}^2=4 \end{gathered}$$