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

Given equation of asymptotes are 3x + 4y = 5 and 4x + 3y = 5

\ Equation of hyperbola is

(3x + 4y – 5) (4x + 3y – 5) = l …(i)

Since, it is passing through origin

\ l = 25

From (i) 12x² + 12y² + 25xy – 35x – 35y = 0.