Joint equation of pair of lines through (3,-2) and parallel to x²-4 x y+3 y²=0 is

Step-by-step solution

Given equation of line is x²-4 x y+3 y²=0 m₁+m₂= 4 3 and m₁ m₂= 1 3 On solving these equations, we get m₁=1, m₂= 1 3 Let the lines parallel to given line are y=m₁ x+c₁ and y=m₂ x+c₂ = 1 3 x+c₁ and y=x+c₂ Also, these lines passes through the point (3,-2) -2= 1 3 3+c₁ c₁=-3 and -2=1 3+c₂ c₂=-5 Required equation of pair of lines is (3 y-x+9)(y-x+5)=0 x²+3 y²-4 x y-14 x+24 y+45=0