Q55 of 59 Page 178

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



We know that,


It is given that the given lines are 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


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