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Question
Find the equation of the hyperbola referred to its principal axes:
whose length of conjugate axis = 12 and passing through (1, – 2)
Solution
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.
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