Angle Between A Pair Of Lines

If θ is an angle between the lines represented by ax2 + 2hxy + by2 = 0, then cos θ = ±

Let ax2 + 2hxy + by2 = 0 represent the two lines

l1x + m1y = 0 ----- (1)

l2x + m2y = 0 ----- (2)

∴ ax2 + 2hxy + by2 = 0 ≡ (l1x + m1y) (l2x + m2y)

Comparing both sides, we have

l1l2 = a;   l1m2 + l2m1 = 2h;   m1m2 = b

If θ is an angle between the lines (1) and (2), then

In particular,if θ is the acute angle between the lines represented by ax2 + 2hxy + by2 = 0, then cos θ =