Question

The eccentricity of the hyperbola 25x² - 9y² = 225 is ______.

Options

• `sqrt34/3`

• 4

• `sqrt34`

• `sqrt34/5`

Answer 1

The eccentricity of the hyperbola 25x² - 9y² = 225 is `underline(sqrt34/3)`.

Explanation:

We have equation of hyperbola 25x² - 9y² = 225

`=> x^2/9 - "y"^2/25 = 1`

On comparing with `x^2/"a"^2 - "y"^2/"b"^2 = 1`, we get

a² - 9, b² = 25

∴ Eccentricity, e = `sqrt(1 + "b"^2/"a"^2)`

`= sqrt(1 + 25/9)`

`= sqrt34/3`