Question

The number of integral values of $\lambda$ for which the equation $x^2+y^2-2\lambda x+2\lambda y+14=0$ represents a circle whose radius cannot exceed $6$, is

• A. $11$
• B. $6$
• C. $12$
• D. $9$

Answer 1

The correct option is A $11$

$x^2+y^2-2\lambda x+2\lambda +14=0$
Radius $=\sqrt{{\lambda }^2+{\lambda }^2-14}$
Given radius $\le 6$
$\sqrt{2{\lambda }^2-14}\le 6$
$2{\lambda }^2-14\le 36$
$2{\lambda }^2-50\le 0$
${\lambda }^2-25\le 0$
$\lambda ϵ[-5,5].$
So, no. of integral values of $\lambda$ are $11$.
$\lambda =-5,-4,-3,-2,-1,0,1,2,3,4,5$