are a,b,c in AP?????

if the lines ax+2y+!=0,bx+3y+!=0 and cx+4y+1=0 passes through the same point then a,b,c are in___________

2 Answers

let the common poit be (h,k)

it must satisfy all lines.

ah+2k+1=0 ---1
bh+3k+1=0 ---2
ch+4k+1=0 ----3

2-1 : (b-a) = -k/h
3-2: (c-b) = -k/h

same difference... therefore a,b,c in A.P. :)

Good work :)

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