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Question
Find the equation of the hyperbola with vertices (0, ± 7), e = `4/3`
Solution
Given that vertices (0, ± 7), e = `4/3`
Clearly, the hyperbola is vertical.
Vertices = (± 0, a)
∴ a = 7 and e = `4/3`
We know that b2 = a2(e2 – 1)
⇒ b2 = `49(16/9 - 1)`
⇒ b2 = `49 xx 7/9`
⇒ b2 = `343/9`
Hence, the equation of the hyperbola is `y^2/49 - (9x^2)/343` = 1
⇒ 9x2 – 7y2 + 343 = 0
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