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 ....

Answer 1

Since, the point of intersection of the coordinate
with the line $\lambda x-y+1=0$ and $x-2y+3=0$ forms the circle
$\therefore (\lambda x-y+1)(x-2y+3)=0$
represents a circle, if coefficient of $x^2$ = coefficient of
and coefficient of $xy=0$
$\Rightarrow \lambda =2$ or $-2\lambda -1=0$
$\Rightarrow \lambda =2$ or $\lambda =-\frac{1}{2}$