Determine the parametric equations for the ellipse centered at $(0, 5)$ with vertices $4$ units up and down from the center and endpoints of the major axis $7$ units to the left and right of the center.

Determine the set of parametric equations for the hyperbola with vertices at $(5, 0)$ and $(-5, 0)$, and foci at $(8, 0)$ and $(-8, 0)$.