Question

Find the eccentricity of the hyperbola 9y² – 4x² = 36.

Answer 1

Given equation is  9y² – 4x² = 36

⇒ `y^2/4 - x^2/9` = 1

Clearly it is a vertical hyperbola.

Where a = 3 and b = 2

We know that b² = a²(e² – 1)

⇒ 4 = 9(e² – 1)

⇒ e² – 1 = `4/9`

⇒ e² = `1 + 4/9 = 13/9`

∴ e = `sqrt(13)/3`

Hence, the required value of e is `sqrt(13)/3`.