SAGAR SINGH - IIT DELHI
Last Activity: 13 Years ago
Dear student,
Let the three given lines be
a1x+b1y+c1=0 ...(i)
a2x+b2y+c2=0 ..(ii)
a3x+b3y+c3=0 ...(iii)
For the given lines to be concurrent, no two of these lines can be parallel or coincident
b1a1
=b2a2
=b3a3
...(iv)
and the point of intersection of any two lines must lie on the third. The point of intersection of (i) and (ii) is
b1c2−b2c1a1b2−a2b1
c1a2−c2a1a1b2−a2b1
(obtain it)
This point must lie on the third line, so we must have
a3
b1c2−b2c1a1b2−a2b1+b3
c1a2−c2a1a1b2−a2b1+c3=0
a3b1c2−a3b2c1+a2b3c1−a1b3c2+a1b2c3−a2b1c3=0