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Question
Find the equation of the hyperbola with vertices (± 5, 0), foci (± 7, 0)
Solution
Given that vertices (± 5, 0), foci (± 7, 0)
Vertex of hyperbola = (± a, 0) and foci (± ae, 0)
∴ a = 5 and ae = 7
⇒ 5 × e = 7
⇒ e = `7/5`
Now b2 = a2(e2 – 1)
⇒ b2 = `25(49/25 - 1)`
⇒ b2 = `25 xx 24/25`
⇒ b2 = 24
The equation of the hyperbola is `x^2/25 - y^2/24` = 1
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