A point P is moving in the plane so that its coordinates after t seconds are (4 cos 2t, 7 sin 2t), measured in feet.
(a) Show that P is following an elliptical path.
(b) Obtain an expression for L, the distance of P from the origin at time t.
(c) How fast is the distance between P and the origin changing when t = π/8? You will need the fact that Du(√u) = 1/(2√2) (see Example 4 or section 2.2).