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Question

If the lines x+2ay+a=0,x+3by+b=0 and x+4cy+c=0 are concurrent, then a,b,c.

A
A.P
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B
G.P
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C
H.P
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D
A.G.P
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Solution

The correct option is A H.P
The given lines are x+2ay+a=0x+3by+b=0x+4cy+c=0
If lines are concurrent then
∣ ∣12aa13bb14cc∣ ∣=0
1(3bc4bc)1(2ac4ac)+1(2ab3ab)=0
ab+bc=2ac
1a+1c=2b
a,b,c are in HP

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