If a circle passes through the points of intersection of the coordinate axes with the lines $\lambda

Question

If a circle passes through the points of intersection of the coordinate axes with the lines $\lambda x-y+1=0$ and $x-2 y+$ $3=0$, then the value of $\lambda$ is

Professor PC Thomas Classes · Answer

The given lines are $\lambda x-y+1=0$ and $x-2 y+3=0$ which meet $x$-axis at $A\left(-\frac{1}{\lambda}, 0ight)$ and $B(-3,0)$ and $y$-axis at $C(0,1)$ and $D\left(0, \frac{3}{2}ight)$ respectively. 。\ Then we must have,\ \ $O A 	imes O B=O C 	imes O D$\ $\Rightarrow\left(-\frac{1}{\lambda}ight)(-3)=1 	imes \frac{3}{2} \Rightarrow \lambda=2$\