The correct option is D a circle having center on the x-axis
z=3(cosθ+2)+i(sinθ)
=3[(cosθ+2)−isinθ](cosθ+2)2+sin2θ
=3(cosθ+2)−isinθ5+4cosθ
=35+4cosθ((cosθ+2)−isinθ)
=a(cosθ+2)−isinθ)
Now
x=a(cosθ+2)
xa−2=cosθ
And y=−asinθ
−ya=sinθ
Hence (xa−2)2+y2a2
=1
(x2−2a)2+y2=a2
Hence it is a circle, centered at (2a,0) where a=35+4cosθ