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  •  If the three distinct lines    <img alt="x+2ay+a=0,x+3by+b=0\: and\: x+4ay+a=0" src="https://learn.careers360.com/latex-image/?x&plus;2ay&plus;a%3D0%2Cx&plus;3by&plu

 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 :

Option: 1

circle
 


Option: 2

hyperbola


Option: 3

  straight line

 


Option: 4

 parabola


Answers (1)

best_answer

As we learnt in 

\begin{vmatrix} 1 &2a &a \\ 1& 3b &b \\ 1& 4a & a \end{vmatrix}

\Rightarrow \left ( 3ab-2ab \right ) -1\left ( 2a^{2} \right )+1 (ab)

\Rightarrow 2ab-2a^{2} =0

    a^{2}-ab=0

    a\left ( a-b \right )=0

Replace (a,b) by (x,y)

x(x-y) = 0

So (a.b) lies on a straight line either x=0 or x=y 

Posted by

sudhir kumar

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