Let the equation of pair of lines y=m₁ x and y=m₂ x can be written as (y-m₁ x ) (y-m₂ x )=0 . Then, the equation of the pair of the angle bisector of the line 3 y^2-5 x y-2 x^2=0 is

Step-by-step solution

Rewriting 3y^2 - 5xy - 2x^2 = 0 as -2x^2 - 5xy + 3y^2 = 0 Comparing with ax^2 + 2hxy + by^2 = 0 : a = -2, 2h = -5 h = - 5 2 , b = 3 Using the angle bisector formula x^2 - y^2 a - b = xy h : x^2 - y^2 -2 - 3 = xy - 5 2 x^2 - y^2 -5 = -2xy 5 x^2 - y^2 = 2xy x^2 - 2xy - y^2 = 0