4 A curve is defined by the parametric equations \(x = 8 \mathrm { e } ^ { - 2 t } - 4 , y = 2 \mathrm { e } ^ { 2 t } + 4\).
- Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in terms of \(t\).
- The point \(P\), where \(t = \ln 2\), lies on the curve.
- Find the gradient of the curve at \(P\).
- Find the coordinates of \(P\).
- The normal at \(P\) crosses the \(x\)-axis at the point \(Q\). Find the coordinates of \(Q\).
- Find the Cartesian equation of the curve in the form \(x y + 4 y - 4 x = k\), where \(k\) is an integer.
(3 marks)