If \( z \) is any complex number satisfying \( |z-k|=k \), where \( k \) is positive real number...
If \( z \) is any complex number satisfying \( |z-k|=k \), where \( k \) is positive real number, then which of the following is correct?
\begin{tabular}{|c|l|c|l|}
\hline \multicolumn{2}{|c|}{ Column-I } & \multicolumn{2}{c|}{ Column-II } \\
\hline A. & \( |\mathrm{z}|_{\max } \) & p. & 0 \\
\hline B. & \( |\mathrm{z}|_{\min } \) & q. & \( : k+\sqrt{k^{2}+1} \) \\
\hline C. & \( |z-i|_{\max } \) & r & \( \sqrt{k^{2}+1}-k \) \\
\hline D. & \( |z-i|_{\min } \) & s. & \( 2 k \) \\
\hline
\end{tabular}
(a) \( \mathrm{A} \rightarrow \mathrm{s} ; \mathrm{B} \rightarrow \mathrm{p} ; \mathrm{C} \rightarrow \mathrm{q} ; \mathrm{D} \rightarrow \mathrm{r} \)
(b) \( \mathrm{A} \rightarrow \mathrm{r} ; \mathrm{B} \rightarrow \mathrm{s} ; \mathrm{C} \rightarrow \mathrm{q} ; \mathrm{D} \rightarrow \mathrm{p} \)
(c) \( \mathrm{A} \rightarrow \mathrm{q} ; \mathrm{B} \rightarrow \mathrm{p} ; \mathrm{C} \rightarrow \mathrm{r} ; \mathrm{D} \rightarrow \mathrm{s} \)
(d) \( \mathrm{A} \rightarrow \mathrm{s} ; \mathrm{B} \rightarrow \mathrm{p} ; \mathrm{C} \rightarrow \mathrm{r} ; \mathrm{D} \rightarrow \mathrm{q} \)
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