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 circlea parabolaan ellipsea straight line

Solution

The correct option is D a straight linex+2ay+a=0     …(1) x+3by+b=0     …(2) x+4ay+a=0     …(3) Solving (1) and (3), y=0,x=−a As given three lines are concurrent, so, (−a,0) will satisfy the equation (2)  −a+b=0 ⇒a=b ∴ Locus of (a,b) is x=y which is a straight line.

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