SOLUTION —
$\because x^2+y^2+\frac{\lambda}{2} x+\frac{9}{4}=0$
$ \text { Now, } \text { radius } =\sqrt{\frac{\lambda^2}{16}-\frac{9}{4}}=0 \\$
$\Rightarrow \lambda = \pm 6 \\$
$\therefore \quad \text { Centre }\left(-\frac{\lambda}{4}, 0\right) =\left( \pm \frac{3}{2}, 0\right)$
So, The correct option of this question will be (A).