9. The complex numbers \(z\) and \(w\) are represented by the points \(P ( x , y )\) and \(Q ( u , v )\) respectively in Argand diagrams and
$$w = z ^ { 2 } - 1$$
- Show that \(v = 2 x y\) and obtain an expression for \(u\) in terms of \(x\) and \(y\).
- The point \(P\) moves along the line \(y = 3 x\). Find the equation of the locus of \(Q\).