If l x 2 + 3 x y - 2 y 2 - 5 x + 5 y + k = 0 represents a pair of perpendicular lines, then

Step-by-step solution

l x 2 + 3 x y - 2 y 2 - 5 x + 5 y + k = 0 if lines are perpendicular then, l - 2 = 0 ⇒ l = 2 2 x 2 + 3 x y - 2 y 2 - 5 x + 5 y + k = 0 it represents a pair of lines a = 2 ,     b = - 2 ,     c = k h = 3 2 ,   f = 5 2 ,     g = - 5 2 a b c + 2 f g h - a f 2 - b g 2 - c h 2 = 0 ⇒ - 4 k - 75 4 - 50 4 + 2 x 25 4 - 9 k 4 = 0 ⇒ 25 k = - 75 ⇒ k = - 3