Question

Lines L₁ ≡ ax + by + c = 0 and L₂ ≡ lx + my + n = 0 intersect at the point P and makes an angle θ with each other. Find the equation of a line L different from L₂ which passes through P and makes the same angle θ with L₁.

Answer 1

Since, the required line L passes through the intersection of L₁ = 0 and L₂ = 0

So, the equation of the required line L is

Which is the required equation of line L.