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A particle moves in the \( x-y \) plane with a constant acceleration \( g \) in the negative \( y \)-direction. Its equation of motion is \( y=a x-b x^{2} \), where \( a \) and \( b \) are constants. Which of the following is/are correct? (A*) The \( x \)-component of its velocity is constant.
(B*) At the origin, the \( y \)-component of its velocity is \( \mathrm{a} \sqrt{\frac{g}{2 b}} \).
\( \left(C^{*}\right) \) At the origin, its velocity makes an angle \( \tan ^{-1}(a) \) with the \( x \)-axis.
-(D*) The particle moves exactly like a projectile.
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