Question

Find the area of the triangle formed by the lines ax² + 2hxy + by² = 0 and lx + my = 1

Answer 1

Let the lines be l₁x + m₁y = 0 and l₂x + m₂y = 0 so that 

l_1ll₂ = a

l₁m₂ + l₁m₁= 2h

and m₁m₂ = b

Suppose the line lx + my = 1 meets these lines at A and B (see Fig.). Substituting y l₁/m₁ in lx + my = 1, we have 

Therefore, the area of ΔOAB is