[Optional 4-4: Coordinate Systems and Parametric Equations] (10 points) In the rectangular coordinate system $xOy$, the parametric equation of curve $C$ is $\left\{\begin{array}{l} x = 3\cos\theta \\ y = \sin\theta \end{array}\right.$ ($\theta$ is the parameter), and the parametric equation of line $l$ is $\left\{\begin{array}{l} x = a + 4t \\ y = 1 - t \end{array}\right.$ ($t$ is the parameter). (1) If $a = -1$, find the coordinates of the intersection points of $C$ and $l$. (2) If the maximum distance from a point on $C$ to line $l$ is $\sqrt{17}$, find $a$.
[Optional 4-4: Coordinate Systems and Parametric Equations] (10 points)
In the rectangular coordinate system $xOy$, the parametric equation of curve $C$ is $\left\{\begin{array}{l} x = 3\cos\theta \\ y = \sin\theta \end{array}\right.$ ($\theta$ is the parameter), and the parametric equation of line $l$ is $\left\{\begin{array}{l} x = a + 4t \\ y = 1 - t \end{array}\right.$ ($t$ is the parameter).
(1) If $a = -1$, find the coordinates of the intersection points of $C$ and $l$.
(2) If the maximum distance from a point on $C$ to line $l$ is $\sqrt{17}$, find $a$.