Question

Find the equation of the hyperbola with vertices (0, ± 7), e = `4/3`

Answer 1

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