Question

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

• A. $2$
• B. $4$
• C. $6$
• D. $3$

Answer 1

The correct option is A $2$

$\lambda x-y+1=0$

at x-axis $\lambda x+1=0$ at y-axis $y=1$

$x=\frac{-1}{\lambda }$ $B(0,1)$

$A(\frac{-1}{\lambda },0)$

For,

$x-2y+3=0$

at x- axis $y=0$ at y-axis $x=0$

So, $x=-3$ $y=\frac{3}{2}$

$(-3,0)$ $(0,3/2)$

Ref. image

$OA\times OC=OB\times OD$

$\frac{-1}{\lambda }\times -3=1\times \frac{3}{2}$

$\lambda =2$