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Question

If the three distinct lines x+2ay+a=0,x+3by+b=0 and x+4ay+a=0 are concurrent, then the point (a,b) lies on a :

A
Circle
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B
Hyperbola
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C
Straight line
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D
Parabola
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Solution

The correct option is B Straight line
∣ ∣12aa13bb14aa∣ ∣=0
(3ab4ab)2a(ab)+a(4a3b)=0
2a22ab=0
(a)(ab)=0
Hence, it lies on a straight line.

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