5 A curve is defined by the parametric equations
$$x = 2 t + \frac { 1 } { t } , \quad y = \frac { 1 } { t } , \quad t \neq 0$$
- Find the coordinates of the point on the curve where \(t = \frac { 1 } { 2 }\).
- Show that the cartesian equation of the curve can be written as
$$x y - y ^ { 2 } = 2$$
- Show that the gradient of the curve at the point \(( 3,2 )\) is 2 .