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Question
Find the equation of the hyperbola referred to its principal axes:
whose vertices are (± 7, 0) and end points of conjugate axis are (0, ±3)
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Solution
Let the equation of the hyperbola referred to its principal axes be
`x^2/"a"^2 - y^2/"b"^2` = 1 ...(1)
Then vertices are (±a, 0) which are given to be (±7, 0).
∴ a = 7
Also, end points of conjugate axes are (0, ±b) which are given to be (0, ±3).
∴ b = 3
∴ by (1), the equation of required hyperbola is `x^2/49 - y^2/9` = 1.
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