Given line is y−2x+1=0......(i) and curve xy+ax+by=0......(ii) Put x=1 in Eq. (i), we get y−2(1)+1=0⇒y=1 From Eq. (i), we get y=2x−1 Put y=2x−1 in Eq. (ii), we get x(2x−1)+ax+b(2x−1)=0 ⇒‌‌2x2+(−1+a+2b)x−b=0 since, Eq. (i) is a tangent to the Eq. (ii). ∴ Discriminant, B2−4AC=0 ∴‌‌(−1+a+2b)2+8b=0.....(iii) Also, point (1,1) satisfy the Eq. (ii) ∴‌‌1×1+a+b=0 ⇒‌‌a=−b−1.....(iv) ∴ From Eqs. (iii) and (iv), we get (−1−b−1+2b)2+8b=0 ⇒‌‌(−2+b)2+8b=0 ⇒‌‌4+b2−4b+8b=0 ⇒‌‌b2+4b+4=0 ⇒‌‌(b+2)2=0⇒b=−2 ∴ From Eq. (iv), we get a=−(−2)−1=1