Let a,b in R and `a^2+ b^2 ne 0 `

Suppose `S={z in C : z =(1)/(alpha +I bt ), t in R, t ne 0 } `where `I= sqrt(-1)` if z=x +iy and `ne S,` then (x,y) lies on

A. the circle with radius `1/(2 alpha)` 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 `