MCQ
If the circles $x^2+y^2+2 \lambda x+2=0$ and $x^2+y^2+4 y+2=0$ touch each other, then $\lambda=$

Answer

Correct option: B.
(B)
The centres of two circles are $C_1(-\lambda, 0)$ and $C _2(0,-2)$ and their radii are $\sqrt{\lambda^2-2}$ and $\sqrt{2}$.
The given circles touches each other, if
$\sqrt{\lambda^2+4}=\sqrt{\lambda^2-2}+\sqrt{2}$
$\Rightarrow \lambda^2+4=\lambda^2-2+2+2 \sqrt{2} \sqrt{\lambda^2-2}$
$\Rightarrow \sqrt{2}=\sqrt{\lambda^2-2}$
$\Rightarrow \lambda^2=4$
$\Rightarrow \lambda= \pm 2$

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