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Question
Find the equation of the hyperbola in the cases given below:
Passing through (5, – 2) and length of the transverse axis along x-axis and of length 8 units
Solution
Transverse axis along x-axis
`x%2/"a"^2 - y^2/"b"^2` = 1
Length of transverse axis 2a = 8
⇒ a = 4
`x^2/16 - y^2/"b"^2` = 1
At (5, – 2) `25/16 - 4/"b"^2` = 1
`25/16 - 1 = 4/"b"^2`
`(25 - 16)/16 = 4/"b"^2`
⇒ `9/16 = 4/"b"^2`
b2 = `(16 xx 4)/9` = 4
Equation of hyperbola `x^2/16 - y^2/(64/9)` = 1
`x%^2/16 - (9y^2)/64` = 1
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