The curve \(C\) has parametric equations \(x=3t^2\), \(y=6t\).
Find the value of \(t\) at the point on \(C\) where the gradient is \(0.4\).[3]
The tangent to \(C\) at the point \(P\), with coordinates \((3p^2,6p)\), meets the \(y\)-axis at \(D\). Find the cartesian equation of the locus of the mid-point of \(PD\) as \(p\) varies.[4]