State whether the statements are true or false.
The lines ax + 2y + 1 = 0, bx + 3y + 1 = 0 and cx + 4y + 1 = 0 are concurrent if a, b, c are in G.P.
Given that ax+2y+1=0 bx+3y+1=0 and cx+4y+1=0 are concurrent .
For the lines to be concurrent
Now expanding along first column we get
a[3-4]-b[2-4]+c[2-3]=0
-a+2b-c=0
2b=a+c and we know that if a, b ,c are in AP then
This means given lines are in AP not in GP
Hence, the given statement is False.