Problem

The hyperbola $H$ is defined by the equation

$$\frac{x^2}{48} - \frac{y^2}{b^2} = 1$$

where $b$ is a positive constant.

Given that $H$ has a focus at the point $(8, 0)$, determine

(i) the value of $b$,

(ii) the exact value of the eccentricity of $H$.