UPSEE Solved Model Paper 7

Any line passing through the intersection of the given lines is
x+3y+4+λ(3x+y+4) = 0 ........ (i)
Or, (1+3λ)x+(3+λ)y+4(1+λ) = 0
The slope of the line m = - 1+3λ/3+λ
As the line is equally inclined with the axes,
m = tan 45° or tan 135° = ±1
∴ - 1+3λ/3+λ = ±1, > λ = ±1
∴ The required lines are (putting λ = - 1, 1 in (i))
x+ 3y + 4 ± (3x+y+4) = 0
Or, x + y + 2 = 0 and x - y = 0