a) Ellipse

b) Parabola

c) Circle

d) Straight line

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$X_{cm}= \large\frac{m_1x_1+m_2x_2}{m_1+m_2}$

$X_1=(4 t+\large\frac{1}{2}$$5t^2)$

$X_2=0$

$X_{cm}=\large\frac{4t+\large\frac{1}{2} 5t^2}{2}$

$Y_{cm}=\large\frac{m_1y_1+m_2y_2}{m_1+m_2}$

$y_1= \large\frac{1}{2}$$5t^2$

$y_2= 4t$

$Y_{cm}=\large\frac{m\bigg(\Large\frac{5}{2} \normalsize+2\bigg)+m(4t)}{m+m}$

$Y_{cm}=\large\frac{4t+\Large\frac{1}{2} \normalsize 5t^2}{2}$

$X_{cm}=Y_{cm}$

Hence centre of mass moves in a straight line

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