Answer:
Option A,C,D
Explanation:
We have, $sz+i\bar{z}+r=0$ ...........(i)
On taking conjugate, $\bar{sz}+\bar{t}z+\bar{r}=0$ ..........(ii)
On solving Eqs. (i) and (ii) , we get
z= $\frac{\bar{r}t-r\bar{s}}{\mid s\mid^{2}-\mid t\mid^{2}}$
(a) For unique solutions of z
${\mid s\mid^{2}-\mid t\mid^{2}}\neq 0 \Rightarrow \mid s \mid\neq \mid t\mid$
It is true.
(b) If $\mid s \mid= \mid t\mid$, then $\bar{r}t-r\bar{s}$ may or may not be zero, So, z may have no solutions.
$\therefore $, L may be an empty set. It is false.
(c)If elements of set L represents the line, then this line and given circle interset at maximum two-point . Hence, it is true
(d) In this case locus of z is a line, so L has infinite elements. Hence, it is true
