5 A particle \(P\) is projected with speed \(u\) at an angle \(\alpha\) above the horizontal from a point \(O\) on a horizontal plane and moves freely under gravity. The horizontal and vertical displacements of \(P\) from \(O\) at a subsequent time \(t\) are denoted by \(x\) and \(y\) respectively.

1. Derive the equation of the trajectory of \(P\) in the form $$\mathrm { y } = \mathrm { x } \tan \alpha - \frac { \mathrm { gx } ^ { 2 } } { 2 \mathrm { u } ^ { 2 } } \sec ^ { 2 } \alpha$$ The point \(Q\) is the highest point on the trajectory of \(P\) in the case where \(\alpha = 45 ^ { \circ }\).
2. Show that the \(x\)-coordinate of \(Q\) is \(\frac { \mathrm { u } ^ { 2 } } { 2 \mathrm {~g} }\).
3. Find the other value of \(\alpha\) for which \(P\) would pass through the point \(Q\).