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 =