Let s, t, r be non-zero complex numbers and L be the set of solutions $z=x+i y(x, y \in \mathrm{R}, i=\sqrt{-1})$ of the equation $s z+t \bar{z}+r=0$, where $\bar{z}=x-i y$. Then, which of the following statement(s) is (are) TRUE ?
Select ALL correct options:
A
If L has exactly one element, then $|s| \neq|t|$
B
If $|s|=|t|$, then L has infinitely many elements
C
The number of elements in $\mathrm{L} \cap\{\mathrm{z}:|\mathrm{z}-1+i|=5\}$ is at most 2
D
If $L$ has more than one element, then $L$ has infinitely many elements
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