1 A curve is defined by the parametric equations
$$x = 1 + 2 t , \quad y = 1 - 4 t ^ { 2 }$$
- Find \(\frac { \mathrm { d } x } { \mathrm {~d} t }\) and \(\frac { \mathrm { d } y } { \mathrm {~d} t }\).
(2 marks) - Hence 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 \(t = 1\).
- Find a cartesian equation of the curve.