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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 
  1. a circle
  2. a parabola
  3. an ellipse
  4. a straight line


Solution

The correct option is D a straight line
x+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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