Question

The number of integral values of $\lambda$ for which $x^2+y^2+\lambda x+(1-\lambda )y+5=0$ is the equation of the circle whose radius cannot exceed $5$, is

• A. $3$
• B. $2$
• C. $1$
• D. none of these

Answer 1

Answer: (D)

none of these

Given equation of circle
$x^2+y^2+\lambda x+(1-\lambda )y+5=0$
${(x+\frac{\lambda }{2})}^2+{(y+\frac{1-\lambda }{2})}^2=-5+\frac{{\lambda }^2}{4}+\frac{{(1-\lambda )}^2}{4}$
Also, given $r\le 5$
$\Rightarrow r^2\le 25$
$\Rightarrow \frac{2{\lambda }^2-2\lambda -19}{4}\le 25$
$\Rightarrow 2{\lambda }^2-2\lambda -119\le 0$