If the lines represented by the equation 2x2−3xy+y2=0 make angles α and β with x - axis, then cot2α+cot2β=
0
3/2
7/4
5/4
m1=tanαandm2=tanβ
⇒cotα=1m1 and cotβ=1m2
Hence, cot2α+cot2β=1m21+1m22=m21+m22(m1m2)2
= (m1+m2)2−2m1m2(m1m2)2=(3)2−2(2)(2)2=54.
If the lines represented by the equation ax2−bxy−y2=0 make angles α and β with the x - axis, then tan(α+β) =