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

• A. $x=5\sec(t),y=\sqrt{39}\tan(t)$
• B. $x=\sqrt{39}\sec(t),y=5\tan(t)$
• C. $x = 8\sec(t), y = 5\tan(t)$
• D. $x=5\tan(t),y=\sqrt{39}\sec(t)$