5 The parametric equations of a curve are
$$x = a \cos ^ { 4 } t , \quad y = a \sin ^ { 4 } t$$
where \(a\) is a positive constant.
- Express \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in terms of \(t\).
- Show that the equation of the tangent to the curve at the point with parameter \(t\) is
$$x \sin ^ { 2 } t + y \cos ^ { 2 } t = a \sin ^ { 2 } t \cos ^ { 2 } t$$
- Hence show that if the tangent meets the \(x\)-axis at \(P\) and the \(y\)-axis at \(Q\), then
$$O P + O Q = a$$
where \(O\) is the origin.