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Question
Find the equation of the hyperbola referred to its principal axes:
whose length of transverse and conjugate axis are 6 and 9 respectively
Solution
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.
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