Question

The circle $x^2+y^2-6x-4y+9=0$ bisects the circumference of the circle $x^2+y^2-(\lambda +4)x-(\lambda +2)y+(5\lambda +3)=0if\lambda$ is equal to

• A. -1
  
• B. 1
  
• C. 2
  
• D. 4

Answer 1

The correct option is D

4

Equation of the common chord is $(\lambda -2)(x+y)+6-5\lambda =0,$ which is a diameter of the 2nd circle if
$(\lambda -2)[\frac{\lambda +4}{2}+\frac{\lambda +2}{2}]+6-5\lambda =0$
$\Rightarrow (\lambda -2)(\lambda +3)+6-5\lambda =0\Rightarrow {\lambda }^2-4\lambda =0$
$\Rightarrow \lambda =0$ or $\lambda =4.$