Question

Find the equation of the hyperbola with vertices (± 5, 0), foci (± 7, 0)

Answer 1

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