6 A curve has cartesian equation \(y ^ { 2 } - x ^ { 2 } = 4\).
- Verify that
$$x = t - \frac { 1 } { t } , \quad y = t + \frac { 1 } { t } ,$$
are parametric equations of the curve.
- Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { ( t - 1 ) ( t + 1 ) } { t ^ { 2 } + 1 }\). Hence find the coordinates of the stationary points of the curve.
Section B (36 marks)