Given, equation of hyperbola 2x 2 + 5xy + 2y 2 + 4x + 5y = 0 and equation of asymptotes

2x 2 + 5xy + 2y 2 + 4x + 5y + λ λ = 0 ...... (i)

which is the equation of a pair of straight line. We know that the standard equation of a pair of straight lines is ax 2 + 2hxy + by 2 + 2gx + 2fy +c = 0. Comparing equation (i) with standard equation, we get a = 2, b = 2, h = 5/2, g = 2, f = 5/2 and c = λ λ .

We also known that the condition for a pair of straight lines is abc + 2fgh - af 2 - bg 2 - ch 2 = 0.

Therefore 4 λ λ + 25 - - 8 - λ λ = 0.

or or λ λ = 2. Substituting value of λ λ in

equation (i), we get

2x 2 + 5xy + 2y 2 + 4x + 5y + 2 = 0.