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Question
Find the equation of the hyperbola referred to its principal axes:
whose distance between foci is 10 and length of conjugate axis 6
Solution
Let the equation of the hyperbola referred to its principal axes be
`x^2/"a"^2 - y^2/"b"^2` = 1 ...(1)
Distance between foci = 2ae = 10
Length of conjugate axis = 2b = 6
∴ ae = 5 and b = 3
b2 = a2(e2 – 1) = a2e2 – a2
∴ 32 = 52 – a2
∴ a2 = 25 – 9 = 16
∴ by (1), the equation of the required hyperbola is `x^2/16 - y^2/9` = 1.
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