If the straight lines x + 2 y = 3 , 2 x + 3 y = 5 and k 2 x + ky = - 1 represent a triangle which is right-angled, then the values of k are k 1 and k 2 . The value of k 1 + k 2 k 1 - k 2 is

Step-by-step solution

Area of triangle ≠ 0 1 2 - 3 2 3 - 5 k 2 k 1 ≠ 0 ⇒ k 2 + k + 1 ≠ 0 ⇒ k ∈ R This should be a right-angled triangle if - 1 2 - k 2 k = - 1 or - 2 3 - k 2 k = - 1 ⇒ k 1 = - 2 or k 2 = - 3 / 2 ∵ k ≠ 0