The ellipse \(E\) has equation \(x ^ { 2 } + 4 y ^ { 2 } = 4\)
(i) Find the coordinates of the foci, \(F _ { 1 }\) and \(F _ { 2 }\), of \(E\).
(ii) Write down the equations of the directrices of \(E\).
Given that the point \(P\) lies on the ellipse, show that
$$\left| P F _ { 1 } \right| + \left| P F _ { 2 } \right| = 4$$
A chord of an ellipse is a line segment joining two points on the ellipse.
The set of midpoints of the parallel chords of \(E\) with gradient \(m\), where \(m\) is a constant, lie on a straight line \(l\).