comparing with trajectory equation

\(y = x \tan \theta-\frac{1}{2} \frac{ gx ^{2}}{ u ^{2} \cos ^{2} \theta}\)

\(\tan \theta=\alpha \Rightarrow \theta=\tan ^{-1} \alpha\)

\(\beta=\frac{1}{2} \frac{ g }{ u ^{2} \cos ^{2} \theta}\)

\(u ^{2}=\frac{ g }{2 \beta \cos ^{2} \theta}\)

Maximum height : \(H\)

\(H =\frac{ u ^{2} \sin ^{2} \theta}{2 g }=\frac{ g }{2 \beta \cos ^{2} \theta} \frac{\sin ^{2} \theta}{2 g }\)

\(H =\frac{\tan ^{2} \theta}{4 \beta}=\frac{\alpha^{2}}{4 \beta}\)