Problem

A hyperbola $H$ has equation

$$\frac{x^2}{a^2}-\frac{y^2}{5}=1$$

where $a$ is a positive constant

The line with equation $x=\frac43$ is a directrix of $H$

(a) Write down an equation of the other directrix.

(b) Determine

(i) the value of $a$

(ii) the coordinates of each of the foci of $H$