Question

The combined equation of the asymptotes of the hyperbola 2x² + 5xy + 2y² + 4x + 5y = 0.

• A. 2x² + 5xy + 2y² = 0
• B. 2x² + 5xy + 2y² - 4x + 5y + 2 = 0
• C. 2x² + 5xy + 2y² + 4x + 5y - 2 = 0
• D. 2x² + 5xy + 2y² + 4x + 5y + 2 = 0

Answer 1

Answer: (D)

2x² + 5xy + 2y² + 4x + 5y + 2 = 0

Answer 2

Given, equation of hyperbola 2x² + 5xy + 2y² + 4x + 5y = 0 and equation of asymptotes

2x² + 5xy + 2y² + 4x + 5y + 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 ax² + 2hxy + by² + 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.

We also known that the condition for a pair of straight lines is abc + 2fgh - af² - bg² - ch² = 0.

Therefore 4λ + 25 - $\frac{25}{2}$ - 8 - $\frac{25}{4}$λ = 0.

or $- \frac{9\lambda}{4} + \frac{9}{2} = 0$ or λ = 2. Substituting value of λ in

equation (i), we get

2x² + 5xy + 2y² + 4x + 5y + 2 = 0.