A curve is defined by the equation \(x ^ { 2 } - y ^ { 2 } = 8\).
Show that at any point \(( p , q )\) on the curve, where \(q \neq 0\), the gradient of the curve is given by \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { p } { q }\).
(2 marks)
Show that the tangents at the points \(( p , q )\) and \(( p , - q )\) intersect on the \(x\)-axis.
(4 marks)
Show that \(x = t + \frac { 2 } { t } , y = t - \frac { 2 } { t }\) are parametric equations of the curve \(x ^ { 2 } - y ^ { 2 } = 8\).
(2 marks)