Question

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

• A. $\frac{1}{2}$
• B. $2$
• C. $1$
• D. $-2$

Answer 1

The correct option is B $2$

Let the lines cut $x-$axis at $A$ and $B$, then $OA=-\frac{1}{\lambda }$ and $OB=-3$

Also if the lines cut the $y-$axis at $C$ and $D$, then $OC=1$ and $OB=\frac{3}{2}$

Now, if the circle passes through $A,B,C,D$

then $OA\times OB\times =OC\times OD\Rightarrow (-\frac{1}{\lambda })(-3)=1\times \frac{3}{2}$ $\Rightarrow \lambda =2$