If a circle passes through the point of intersection of the lines `lambdax- y +1=0` and `x-2y+3=0` with the coordinate axis, then value of `lambda` is

Answer

`lambda=2`

Explanation

Line `lambdax-y+1` meets x-axis at `A (- 1// lambda,0)` and y-axis `D (0,1)`.
Line `x-2y+3=0` meets x-axis at `B (-3,0)` and y-axis at `D(0,3//2)`.
Since points B,A,C and D lie on a circle, we must have
`OAxx OB = OC xx OD`
`implies (1)/(lambda)xx3=1 xx (3)/(2)`
`implies lambda =2`