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 any subsequent time \(t\) are denoted by \(x\) and \(y\), respectively.

(a) Derive the equation of the trajectory of \(P\) in the form \(y=x\tan\alpha-\dfrac{gx^2}{2u^2}\sec^2\alpha\).

It is given that \(u=20\sqrt2\,\text{m s}^{-1}\) and that \(P\) passes through the point where \(x=64\,\text{m}\) and \(y=8\,\text{m}\).

(b) Find the possible values of \(\tan\alpha\).