8 The parametric equations of a curve are
$$x = \tan ^ { 2 } 2 t , \quad y = \cos 2 t$$
for \(0 < t < \frac { 1 } { 4 } \pi\).
- Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = - \frac { 1 } { 2 } \cos ^ { 3 } 2 t\).
\includegraphics[max width=\textwidth, alt={}, center]{9da6c2ac-31aa-4063-88b9-e15e38bedd8a-10_2716_38_109_2012}
\includegraphics[max width=\textwidth, alt={}, center]{9da6c2ac-31aa-4063-88b9-e15e38bedd8a-11_2725_35_99_20} - Hence find the equation of the normal to the curve at the point where \(t = \frac { 1 } { 8 } \pi\). Give your answer in the form \(y = m x + c\).