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. 18
• C. 16
• D. none of these

Answer 1

The correct option is C 16

$\sqrt{\{\frac{{\lambda }^2}{4}+\frac{(1-\lambda {)}^2}{4}-5\}}\le 5\Rightarrow {\lambda }^2+(1-\lambda {)}^2-20\le 100\Rightarrow 2{\lambda }^2-2\lambda -119\le 0\therefore \frac{1-\sqrt{239}}{2}\le \lambda \le \frac{1+\sqrt{239}}{2}\Rightarrow -7.2\le \lambda \le 8.2(approx.)\Rightarrow \lambda =-7,-6,-5,.....,7,8$