An ellipse in space

An ellipse is specified parametrically as

$\mathbf{p}(t) = \mathbf{r_C} + \mathbf{v_1} \cos t + \mathbf{v_2} \sin t$

where $\mathbf{r_C} = (10, 5, -10) , \mathbf{v_1} = (8,4,1)$ and $\mathbf{v_2} = (-2,3,4)$ . Find the minimum and maximum distance from any point on the ellipse to the fixed point $\mathbf{p_0} = (5,10, 15)$ . Report the sum of the minimum and maximum distances.