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Question
Find the equation of the hyperbola referred to its principal axes:
whose length of transverse axis is 8 and distance between foci is 10
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Solution
Let the required equation of hyperbola be
`x^2/"a"^2 - y^2/"b"^2` = 1.
Length of transverse axis = 2a
Given, length of transverse axis = 8
∴ 2a = 8
∴ a = 4
∴ a2 = 16
Distance between foci = 2ae
Given, distance between foci = 10
∴ 2ae = 10
∴ ae = `10/2` = 5
∴ a2e2 = 25
Now, b2 = a2(e2 – 1)
∴ b2 = a2e2 – a2
∴ b2 = 25 – 16 = 9
∴ The required equation of hyperbola is `x^2/16 - y^2/9` = 1.
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