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 \( i=\sqrt{-1} \).
\( \mathrm{P} \)
If \( \mathrm{z}=\mathrm{x}+ \) iy and \( \mathrm{z} \in \mathrm{S} \), then \( (\mathrm{x}, \mathrm{y}) \) lies on
W
(A) the circle with radius \( \frac{1}{2 \mathrm{a}} \) and centre \( \left(\frac{1}{2 \mathrm{a}}, 0\right) \) for \( \mathrm{a}0, \mathrm{~b} \neq 0 \)
(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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