If the bisectors of the pair of lines x 2 - 2 m x y - y 2 = 0 is represented by x 2 - 2 n x y - y 2 = 0 , then

Step-by-step solution

Given equation is x 2 - 2 m x y - y 2 = 0     . . . . . 1 Compare the given equation with a x 2 + 2 h x y + b y 2 = 0     . . . . . . 2 We have, a = 1 , h = - m and b = - 1 Now the equation of the bisector of the angle between the pair of lines in equation 1 is x 2 - y 2 a - b = x y h ⇒ x 2 - y 2 1 - - 1 = x y - m ⇒ - m x 2 + m y 2 = 2 x y ⇒ m x 2 - m y 2 + 2 x y = 0 Now on comparing this equation with x 2 - 2 n x y - y 2 = 0 We get, m = 1 , n = - 1 So option 1 is correct.