9. The complex numbers \(z\) and \(w\) are represented by the points \(P ( x , y )\) and \(Q ( u , v )\) respectively, in Argand diagrams, and \(w = 1 - z ^ { 2 }\).
- Find expressions for \(u\) and \(v\) in terms of \(x\) and \(y\).
- The point \(P\) moves along the line \(y = 4 x\). Find the equation of the locus of \(Q\).
- Find the perpendicular distance of the point corresponding to \(z = 2 + 5 \mathrm { i }\) in the \(( u , v )\)-plane, from the locus of \(Q\).