Question

Find the equation of the hyperbola referred to its principal axes:

whose length of conjugate axis = 12 and passing through (1, – 2)

Answer 1

Let the equation of the hyperbola referred to principal axes be `x^2/"a"^2 - y^2/"b"^2` = 1    ...(1)

Length of conjugate axes = 2b = 12

∴ b = 6

The hyperbola passes through (1, – 2)

∴ `1^2/"a"^2 - (-2)^2/6^2` = 1 ........[∵ b = 6]

∴ `1/"a"^2 = 1 + 1/9 = 10/9`

∴ a² = `9/10`

∴ by (1), the equation of the required hyperbola is `x^2/((9/10)) - y^2/36` = 1

∴ `(10x^2)/9 - y^2/36` = 1.