Question

Prove that the straight lines (a+b)x + (a-b)y =2ab , (a-b)x + (a+b)y = 2ab and x+y =0 , form an isosceles triangle whose vertical angle is 2tan^-1(a/b).

Answer 1

Second line given as: (a - b)x + (a - b)y = 2ab
==> x + y = 2ab/(a - b) --------- (1)

3rd line given as: x + y = 0 -------- (2)

Lines at (1) & (2) are parallel. So two parallel lines can't form a triangle.