Question

If lines whose equation are y = m₁ + c₁y = m₂x + c₂ and y = m₅x + c₃ meet is a point then prove that m₁( (c₂ – c₃) + m₂ (c₃ – c₁) + m₃(c₁ – c₂) = 0

Answer 1

The equation of the given lines are 

m₁x – y + c₁ = 0 ……. (1) 

m₂x – y + c₂ = 0 …… (2) 

m₃x – y + c₃ = 0 .. (3)

The three lines will be concurrent if the point of intersection of (1) and (2) lies on (3)