If the line y = m x is one of the bisectors of x 2 + 4 x y - y 2 = 0 , then value of 2 m =

Step-by-step solution

Given: x 2 + 4 x y - y 2 = 0 This is the equation of pair of straight lines so comparing it with a x 2 + 2 h x y + b y 2 = 0 we get, a = 1 ,   b = - 1 ,   h = 2 As we know the equation of the bisector is given by, x 2 - y 2 a - b = x y h ⇒ x 2 - y 2 1 - - 1 = x y 2 ⇒ x 2 - x y - y 2 = 0 As y = m x is one of the bisector ⇒ x 2 - x m x - m x 2 = 0 ⇒ x 2 - m x 2 - m 2 x 2 = 0 ⇒ m 2 + m - 1 = 0 ⇒ m = - 1 ± 5 2 ⇒ 2 m = - 1 ± 5