Question

The equation of the transverse and conjugate axes of a hyperbola are respectively 3x + 4y – 7 = 0, 4x – 3y + 8 = 0 and their respective lengths are 4 and 6. The equation of the hyperbola is

a. 17x² + 312xy + 108y² – 634x – 312y – 715 = 0

b. 108x² + 312xy + 17y² – 312x – 634y – 715 = 0

c. 108x² – 312xy + 17y² – 312x – 634y – 715 = 0

d. none of these

Answer 1

a. 17x² + 312xy + 108y² – 634x – 312y – 715 = 0

The equations of hyperbola is

9(9x² + 16y² + 49 + 24xy – 42x – 56y) – 4(16x² + 9y² + 64 – 24xy + 64x – 48y) = 900

17x² + 312xy + 108y² – 634x – 312y – 715 = 0