Let 0 ne a, 0 ne b in R. Suppose S={z ...

Let `0 ne a, 0 ne b in R`. Suppose
`S={z in C, z=1/(a+ibt)t in R, t ne 0}`, where `i=sqrt(-1)`. If `z=x+iy` and `z in S`, then `(x,y)` lies on

A

the circle with radius `1/(2a)` and centre `(1/(2a),0)` for `a gt 0, b ne 0`

B

the circle with radius `-1/(2a)` and centre`(-1/(2a),0)` for `a lt 0,b ne 0`

C

the X-axis for `a ne 0,b=0`

D

the Y-axis for `a=0, b ne 0`

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The correct Answer is:

A, C, D

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