If the lines represented by the equation ax2−bxy−y2=0 make angles α and β with the x - axis, then tan(α+β) =
Here the equation is ax2−bxy−y2=0 and given that m1=tanα and m2=tanβ and we know that
m1+m2=b−1=tanα+tanβ
and m1m2=a−1=tanαtanβ
tan(α+β)=tanα+tanβ1−tanαtanβ=−b1−(−a)=−b(1+a).