Question

The limiting points of the system of circles represented by the equation $2\left(x^2+y^2\right)+\lambda x+9 / 2=0$ are

(a) $\left( \pm \frac{3}{2}, 0\right)$

(b) $(0,0)$ and $\left(\frac{9}{2}, 0\right)$

(c) $\left( \pm \frac{9}{2}, 0\right)$

(d) $( \pm 3,0)$

Answer 1

$\because x^2+y^2+\frac{\lambda}{2} x+\frac{9}{4}=0$

$ \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).