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Answer :

[tex]\begin{gathered} y=\cot (\frac{1}{4}x)=0 \\ x=2(n-1)\pi \\ n\in N \end{gathered}[/tex]

The asymptotes are:

[tex]\frac{x}{4\pi}\notin Z[/tex]

So, the midpoints are:

[tex]\begin{gathered} \frac{0+2\pi}{2}=\pi \\ \frac{0-2\pi}{2}=-\pi \end{gathered}[/tex][tex]\begin{gathered} (\pi,5) \\ (-\pi,-5) \end{gathered}[/tex]

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