Figure shows the initial position of a system of two particles. Given that centre of mass of the system remains at rest particle `A` moves i a trajectory givenn by `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1`
Pick the correct option (s) for the nature of `B's` trajectory and the coordinates of `B` at the instant when `A` was at the position `(0,b)`.

Options

A. Trajectory of `B` is elliptical
B. Trajectory of `B` is circular
C. `(0,(-b)/2)`
D. `(a/2,(-b)/2)`

Answer

A, D

Explanation

`(2mx_(B)+mx_(A))/(3m)=a/3impliesx_(A)=a-2x_(B)`
`(2my_(B)+my_(A))/(3m)=0impliesy_(A)=2y_(B)`
Trajectory of `B` is `((a-2x)^(2))/(a^(2))+((2y)^(2))/(b^(2))=1`