\[(a)\;y=2x-5x^2 \quad (b)\;y=x-5x^2 \quad (c)\;4y=2x-5x^2\quad (d)\;y=2x-25 x^2\]

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From given velocity

$\tan {\theta}=\large\frac{y \; componet}{x \;component}$

$\qquad=\large\frac{2}{1}$

$\qquad=2$

Therefore $ \cos \theta=\large\frac{1}{\sqrt 5}$

$y=x \tan \theta-\large\frac{gx^2}{2u^2\cos ^2 \theta}$

$\quad= x(2)-\large\frac{10 (x^2)}{2\bigg( \sqrt {2^2+1^2}\bigg)^2 \bigg(\Large\frac{1}{\sqrt 5}\bigg)^2}$

$y=2x-5x^2$

Hence a is the correct answer.

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