Question

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

• A. $2$
• B. $1/3$
• C. $6$
• D. $3$

Answer 1

Answer: (A), (B)

The correct options are
A $2$
B $1/3$

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

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