The trajectory of a projectile in a vertical plane is y = ax - bx², 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

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

• C

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

• D

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