Given lines, ‌x+2y+λ=0....(i) ‌2x2−2xy+3y2+2x−y−1=0....(ii) From Eqs. (i) ‌
x+2y
−λ
=1 Now, homogenizing the Eq. (ii) ‌⇒‌‌2x2−2xy+3y2+(2x−y)(‌
x+2y
−λ
) ‌‌‌−(‌
x+2y
−λ
)2=6 ‌⇒‌‌(2λ2−2λ−1)x2+(−2λ2−3λ−4)xy+(3λ2+2λ−4)y2=0 For lines to be ⟂′r ⇒‌‌2λ2−2λ−1+3λ2+2λ−4=0 ‌λ=±1⇒λ=1