2 A curve is defined by the parametric equations
$$x = \frac { 1 } { t } , \quad y = t + \frac { 1 } { 2 t }$$
- Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in terms of \(t\).
- Find an equation of the normal to the curve at the point where \(t = 1\).
- Show that the cartesian equation of the curve can be written in the form
$$x ^ { 2 } - 2 x y + k = 0$$
where \(k\) is an integer.