Question

The eccentricity of the hyperbola x² – 3y² = 2x + 8 is ______.

Options

• `2/3`

• `1/3`

• `2/sqrt(3)`

• `3/2`

Answer 1

The eccentricity of the hyperbola x² – 3y² = 2x + 8 is `underlinebb(2/sqrt(3))`.

Explanation:

The given equation reduces to `(x - 1)^2/9 - y^2/3` = 1.

Thus a² = 9, b² = 3

Using b² = a² (e² – 1), we get

3 = 9(e² – 1) `\implies` e = `2/sqrt(3)`.