If the lines `a x+2y+1=0,b x+3y+1=0a n dc x+4y+1=0` are concurrent, then `a ,b ,c` are in (a). A.P. (b). G.P. (c). H.P. (d). none of these

Options

A. A.P.
B. G.P.
C. H.P.
D. none of these

Answer

C

Explanation

Given lines will be concurrent , if
`|{:(1,2a,a),(1,3b,b),(1,4c,c):}|=0`
`implies -bc+2ac-ab=0 implies b =(2ac)/(a+c) implies a,b,c` are in H.P.