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 a circle whose radius cannot exceed 5 is

• A. 14
• B. 16
• C. 18

Answer 1

The correct option is A 14

$\sqrt{\frac{x^2}{4}+\frac{(1-\lambda {)}^2}{4}-5}\le 5$
$\Rightarrow {\lambda }^2+(\lambda -1{)}^2-20\le 100\Rightarrow 2{\lambda }^2-119\le 0$
$\therefore \frac{1-\sqrt{239}}{2}\le \lambda \le \frac{1+\sqrt{239}}{2}$
$\lambda ϵ[-7.2,8.2]\Rightarrow \lambda ϵ[-7,8]$