N2017 P2 Q1

A curve \(C\) has parametric equations \[x=\dfrac3t,\qquad y=2t.\]

1. The line \(y=2x\) cuts \(C\) at the points \(A\) and \(B\). Find the exact length of \(AB\).[3]
2. The tangent at the point \(P\left(\dfrac3p,2p\right)\) on \(C\) meets the \(x\)-axis at \(D\) and the \(y\)-axis at \(E\). The point \(F\) is the midpoint of \(DE\). Find a cartesian equation of the curve traced by \(F\) as \(p\) varies.[5]