Find the centre, eccentricity, foci and directrices of the hyperbola

$x^2-3y^2-2x=8$

Find the equation of the hyperbola, referred to its principal axes as axes of coordinates, in the following case:

The distance between the foci $=16$ and eccentricity $=\sqrt{2}$

Find the equation of the hyperbola, referred to its principal axes as axes of coordinates, in the following case:

conjugate axis is $5$ and the distance between foci $=13$

Find the equation of the hyperbola, referred to its principal axes as axes of coordinates, in the following case:

conjugate axis is $7$ and passes through the point $(3,-2)$

Find the equation of the hyperbola whose foci are $(6,4)$ and $(-4,4)$ and eccentricity is $2$.