Q. If angle between the lines belonging to the family of lines $(x + 3 y - 7) + λ (x + y - 3) = 0$ and $(3 x + y - 7) +$ $μ (x + y - 3) = 0$ which are farthest from origin is $θ$ . If $tan θ = \frac{p}{q}$ (p, q are coprime) then find $p + q$ . (where $λ$ and $μ$ are real parameters).

100 98 Straight Lines Report Error

Answer: 7

Q. If angle between the lines belonging to the family of lines (x+3y−7)+λ(x+y−3)=0 and (3x+y−7)+ μ(x+y−3)=0 which are farthest from origin is θ. If tanθ=qp​ (p, q are coprime) then find p+q. (where λ and μ are real parameters).