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Question

Find value of λ for which line y=x+1,y=λx+2 and y=(λ2+λ1)x+3 are con-current.

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Solution

3linesareconcurrentifthepointofinstructionof2linesliesonthethirdliney=x+1(1)y=λx+2(2)y=(λ2+λ1)x+3(3)solvingequation(1)and(2)x=11λy=2λ1λ(11λ,2λ1λ)mustsatisfyequation(3)2λ1λ=(λ2+λ1)×11λ+3λ2λ=0λ(λ1)=0λ=0,1λcantbe1aspointofintersectionhas1λasitsdenominator

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