Let \( a, b \in R \) and \( a^{2}+b^{2} \neq 0 \). Suppose \( S=\le...

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Let \( a, b \in R \) and \( a^{2}+b^{2} \neq 0 \).
Suppose \( S=\left\{z \in C: z=\frac{1}{a+i b t}, t \in R, t \neq 0\right\} \), where
\( \mathrm{P} \)
W
\( i=\sqrt{-1} \). If \( z=x+i y \) and \( z \in S \), then \( (x, y) \) lies on
[JEE Advanced 2016 4M]
(a) the circle with radius \( \frac{1}{2 a} \) and centre \( \left(\frac{1}{2 a}, 0\right) \) for \( a0, b \neq 0 \)
(b) the circle with radius \( -\frac{1}{2 a} \) and centre \( \left(-\frac{1}{2 a}, 0\right) \) for
\[
a0, b \neq 0
\]
(c) the \( X \)-axis for \( a \neq 0, b=0 \)
(d) the \( Y \)-axis for \( a=0, b \neq 0 \)
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