Solve for trajectory (if you can)

We have placed a particle of mass \(m\) at \(\overset { \rightarrow }{ r } ={ r }_{ 0 }\hat { i }\).

At \(t=0\) we have given it a velocity of \(\overrightarrow { v } ={ v }_{ 0 }\hat { j }\).In the whole co-ordinate plane the force is given by \(\overrightarrow{F}=\frac { -8 }{ { r }^{ 3 } } \overrightarrow { r }N\)

The title says solve for trajectory but I am telling you that the trajectory of the particle is ellipse.If the eccentricity of the ellipse is given by \(e=\frac { a }{ b }\) where \(a,b\) are co-prime integers then find \(a\times b\)

Details and Assumptions:

1)\({ v }_{ 0 }=1m/s,{ r }_{ 0 }=2metre,m=1Kg\)

2)There are no other force acting on the particle except the force given.

3) Ignore gravity

Also try Solve for trajectory again.
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