The ratio in which the line 3 x+4 y+2=0 divides the distance between the lines 3 x+4 y+5=0 and 3 x+4 y-5=0 is

Step-by-step solution

The given lines are parallel, represented by the equations 3x + 4y + 5 = 0 , 3x + 4y + 2 = 0 , and 3x + 4y - 5 = 0 . Let the lines be L₁: 3x + 4y + 5 = 0 , L₂: 3x + 4y + 2 = 0 , and L₃: 3x + 4y - 5 = 0 . The distance between two parallel lines ax + by + c₁ = 0 and ax + by + c₂ = 0 is given by d = |c₁ - c₂| a^2 + b^2 . The distance d₁ between L₁ and L₂ is d₁ = |5 - 2| 3^2 + 4^2 = 3 5 . The distance d₂ between L₂ and L₃ is d₂ = |2 - (-5)| 3^2 + 4^2 = 7 5 . The ratio in which L₂ divides the distance between L₁ and L₃