Consider the \(A\) parameter of the long line given by \(\cosh \theta\), where \(\theta=\) \(\sqrt{Z Y}\). With \(x=e^{-\theta}=x_{1}+j \mathrm{x}_{2}\) and \(A=\mathrm{A}_{1}+j \mathrm{~A}_{2}\), show that \(x_{1}\) and \(x_{2}\) satisfy the following:

\[
x_{1}^{2}-x_{2}^{2}-2\left(\mathrm{~A}_{1} x_{1}-\mathrm{A}_{2} x_{2}ight)+1=0
\]

and \(x_{1} x_{2}-\left(\mathrm{A}_{2} x_{1}+\mathrm{A}_{1} x_{2}ight)=0\).