Question

Equation of hyperbola passing through origin and whose asymptotes are 3x + 4y = 5 and 4x + 3y = 5, is:

• A. x² - y² = 1
• B. 12x² + 12y² + 35xy - 15x - 15y = 0
• C. 12x² + 12y² + 25xy - 35x - 35y = 0
• D. 12x² + 12y² + 25xy - 25x - 25y = 0

Answer 1

Answer: (C)

12x² + 12y² + 25xy - 35x - 35y = 0

Answer 2

(3x + 4y - 5) (4x + 3y - 5) = λ is family of hyperbola have given asymptotes as it passes through origin λ = 25.

12x² + 12y² + 25xy - 35x - 35y = 0.