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