The ends \(A\) and \(B\) of a rod of fixed length move on the positive \(x\) and \(y\) axes respectively. \(C\) is a point on \(AB\), and \(CD\) is perpendicular to \(AB\), as shown in the figure. The lengths of \(AC\), \(BC\) and \(CD\) are \(a\), \(b\) and \(c\) respectively.

- Find parametric equations for the locus of \(C\).
- Find parametric equations for the locus of \(D\).
- If \(c^2=ab\) show that the locus of \(D\) consists of part of a straight line and find the coordinates of the extremities of this locus.
- Sketch the loci of \(C\) and \(D\) for the case \(a=4\), \(b=9\), \(c=6\).