Let $a, b \in R$ and $a^2+b^2 \neq 0$. Suppose $S=\left\{z \in C: \frac{1}{a+i b t}, t \in R, t \neq 0\right\}$; where $i=\sqrt{-1}$. If $z=x+i y$ and $z \in S$, then $(x, y)$ lies on
Select ALL correct options:
A
the circle with radius $\frac{1}{2 a}$ and centre $\left(\frac{1}{2 a}, 0\right)$ for $a>0, b \neq 0$
B
the circle with radius $-\frac{1}{2 a}$ and centre $\left(-\frac{1}{2 a}, 0\right)$ for $a<0, b \neq 0$
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