Let $$a, b \epsilon R$$ and $$a^2 + b^2 \neq 0$$. Suppose $$S = \left\{z \epsilon C : z = \frac{1}{a + ibt}, t \epsilon R, t \neq 0\right\}$$, where $$i = \sqrt{-1}$$. If $$z = x + iy$$ and $$z \epsilon S$$, then (x, y) lies on

A

the circle with radius $$\frac{1}{2a}$$ and center $$\left(\frac{1}{2a}, 0\right)$$ for $$a > 0, b \neq 0$$

B

the circle with radius $$-\frac{1}{2a}$$ and center $$\left(-\frac{1}{2a}, 0\right)$$ for $$a < 0, b \neq 0$$

C

the x-axis for $$a \neq 0, b = 0$$

D

the y-axis for $$a = 0, b \neq 0$$