Let $\mathrm{z}_{1}=2+3 \mathrm{i}$ and $\mathrm{z}_{2}=3+4 \mathrm{i}$. The set $\mathrm{S}=\left\{\mathrm{z} \in \mathrm{C}:\left|\mathrm{z}-\mathrm{z}_{1}\right|^{2}-\left|\mathrm{z}-\mathrm{z}_{2}\right|^{2}=\left|\mathrm{z}_{1}-\mathrm{z}_{2}\right|^{2}\right\}$ represents a

Let $\mathrm{z}_{1}=2+3 \mathrm{i}$ and $\mathrm{z}_{2}=3+4 \mathrm{i}$. The set $\mathrm{S}=\left\{\mathrm{z} \in \mathrm{C}:\left|\mathrm{z}-\mathrm{z}_{1}\right|^{2}-\left|\mathrm{z}-\mathrm{z}_{2}\right|^{2}=\left|\mathrm{z}_{1}-\mathrm{z}_{2}\right|^{2}\right\}$ represents a [JEE (Main) 25 Jan 2023 S I]
\begin{itemize}
\item[(A)] hyperbola with the length of the transverse axis 7
\item[(B)] straight line with the sum of its intercepts on the coordinate axes equals -18
\item[(C)] hyperbola with eccentricity 2
\item[(D)] straight line with the sum of its intercepts on the coordinate axes equals 14
\end{itemize}