Is it Analytically Complex?

Let $s,t,r$ be non-zero complex numbers and $L$ be the solution set of the equation $sz+t\bar z+r=0$ where $z=x+iy,\bar z=x-iy,i=\sqrt{-1},$ and $x,y$ are real numbers .Then which of the following statement(s) is(are) TRUE ?

$1)$ If $L$ has exactly one element, then $|s|\neq|t|$

$2)$ If $|s|=|t|$ , then $L$ has infinitely many elements

$3)$ The number of elements in $L\cap \{z:|z-1+i|=5\}$ is at most $2$

$4)$ If $L$ has more than one element, then $L$ has infinitely many elements

Input the answer in increasing order . For example if options $4,2,3$ are correct then input the answer as $234$ .