7 A curve is given parametrically by the equations
$$x = t ^ { 2 } , \quad y = \frac { 1 } { t }$$
- Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in terms of \(t\), giving your answer in its simplest form.
- Show that the equation of the tangent at the point \(P \left( 4 , - \frac { 1 } { 2 } \right)\) is
$$x - 16 y = 12$$
- Find the value of the parameter at the point where the tangent at \(P\) meets the curve again.