- The ellipse \(E\) has equation
$$\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 16 } = 1$$
The points \(S\) and \(S ^ { \prime }\) are the foci of \(E\).
- Find the coordinates of \(S\) and \(S ^ { \prime }\)
- Show that for any point \(P\) on \(E\), the triangle \(P S S ^ { \prime }\) has constant perimeter and determine its value.