5 A curve is defined by the parametric equations \(x = 2 t + \frac { 1 } { t ^ { 2 } } , \quad y = 2 t - \frac { 1 } { t ^ { 2 } }\).
- At the point \(P\) on the curve, \(t = \frac { 1 } { 2 }\).
- Find the coordinates of \(P\).
- Find an equation of the tangent to the curve at \(P\).
- Show that the cartesian equation of the curve can be written as
$$( x - y ) ( x + y ) ^ { 2 } = k$$
where \(k\) is an integer.