Question

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

whose length of transverse and conjugate axis are 6 and 9 respectively

Answer 1

Let the equation of the hyperbola referred to its principal axes be

`x^2/"a"^2 - y^2/"b"^2` = 1      ...(1)

Then length of transverse axis = 2a = 6

and length of conjugate axis = 2b = 9

∴ a = 3, b = `9/2`

∴ by (1), the equation of required hyperbola is

`x^2/9 - y^2/((81/4))` = 1

∴ `x^2/9 - (4y^2)/81` = 1.