Question

If $2(x^2+y^2)+4\lambda x+{\lambda }^2=0$ represents a circle of meaningful radius, then the range of real values of $\lambda$ is

• A. $R$
• B. $(0,\infty )$
• C. $(-\infty ,0)$
• D. $(-\infty ,0)\cup (0,\infty )$

Answer 1

Answer: (D)

$(-\infty ,0)\cup (0,\infty )$

$x^2+y^2+2\lambda x+\frac{{\lambda }^2}{2}=0$
Radius $=\sqrt{{\lambda }^2-\frac{{\lambda }^2}{2}}=\left|\frac{\lambda }{\sqrt{2}}\right|$
So, for meaningful radius.
$\lambda ϵR-\left\{0\right\}.$