• if a circle passes through the points of intersection of lines 2x - y +1 = 0 and x + Ly - 3 = 0 with the axes of reference then value of L is
• ans is 2

Dear student,

The point of intersection of the line   2x -y+1 =0 with the coordinate axes are A(-1/2,0), B (0,1) 

The point of intersection of the line   x + Ly - 3  =0 with the coordinate axes are C(3,0),  D(0,3/L)
 
since A, B, C, D  are concyclic we have 

OA . OC = OB.OD
 $$\begin{gathered} \left|\frac{1}{2}\right|\times \left|3\right| =\left|1\right|\times \left|\frac{3}{L}\right| \\ \frac{3}{2}=3\left|\frac{1}{L}\right| \\ \left|L\right|=2 \\ L = \pm 2 \\ But when L=2 B and D will not lie on the circle simul\tan eously \\ \therefore L= -2 \end{gathered}$$


  Regards