Question

The equation of the hyperbola which has 3x – 4y + 7 = 0 and 4x + 3y + 1 = 0 as its asymptotes and which passes through the origin is

a. x² – y² = 12xy

b. 12x² – 7xy – 12y² + 31x + 17y = 0

c. 12x² – 12y² = 7xy

d. 12x² + 7xy – 12y² + 25x – 19y = 0

Answer 1

Correct option is b. 12x² – 7xy – 12y² + 31x + 17y = 0

Combined equation of the asymptotes is

(3x – 4y + 7) (4x + 3y + 1) = 0

12x² – 7xy – 12y² + 31x + 17y + 7 = 0

Since equation of hyperbola and combined equation of its asymptotes differ by a constant, therefore equation of hyperola may be

12x² – 7xy – 12y² + 31x + 17y + c = 0

But it passes through the origin. So c = 0

Hence equation of hyperbola is

12x² – 7xy – 12y² + 31x + 17y = 0