The trajectory of a projectile in a vertical plane is $y=ax-b{x}^2,$ where a and b are constants and x and y are respectively horizontal and vertical distances of the projectile from the point of projection. The maximum height attained by the particle and the angle of projection from the horizontal are :

• A

  $\frac{{\mathrm{b}}^2}{2\mathrm{a}}, {\tan }^{-1}\left(\mathrm{b}\right)$

• B

  $\frac{{\mathrm{b}}^2}{4\mathrm{a}}, {\tan }^{-1}\left(\mathrm{b}\right)$

• C

  $\frac{{\mathrm{a}}^2}{4\mathrm{b}},{\tan }^{-1}\left(\mathrm{a}\right)$

• D

  $\frac{2{\mathrm{a}}^2}{\mathrm{b}}, {\tan }^{-1}\left(\mathrm{a}\right)$