Let the equation of the pair of lines y=p x and y=q x can be written as (y-p x)(y-q x)=0 . Then the equation of the pair of the angle bisectors of the line x^2-4 x y-5 y^2=0 is

Step-by-step solution

The given equation of the pair of lines is x^2 - 4xy - 5y^2 = 0 . Comparing this with the general homogeneous equation of the second degree ax^2 + 2hxy + by^2 = 0 , we have a = 1 , 2h = -4 (so h = -2 ), and b = -5 . The equation of the pair of angle bisectors is given by the formula x^2 - y^2 a - b = xy h . Substituting the values of a , b , and h into the formula: x^2 - y^2 1 - (-5) = xy -2 x^2 - y^2 6 = xy -2 Multiplying both sides by 6: x^2 - y^2 = -3xy x^2 + 3xy - y^2 = 0 . Answer: x^2+3 x y-y^2=0