6 The parametric equations of a curve are
$$x = a \cos ^ { 3 } t , \quad y = a \sin ^ { 3 } t$$
where \(a\) is a positive constant and \(0 < t < \frac { 1 } { 2 } \pi\).
- 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
$$x \sin t + y \cos t = a \sin t \cos t$$
- Hence show that, if this tangent meets the \(x\)-axis at \(X\) and the \(y\)-axis at \(Y\), then the length of \(X Y\) is always equal to \(a\).