Question

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

• A. 2
• B. 4
• C. 5
• D. 8

Answer 1

The correct option is A 2

Let the lines cuts 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 passing through $A,B,C$ and $D$ then

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