Solve for trajectory (if you can)

We have placed a particle of mass mm at r=r0i^\overset { \rightarrow }{ r } ={ r }_{ 0 }\hat { i }.

At t=0t=0 we have given it a velocity of v=v0j^\overrightarrow { v } ={ v }_{ 0 }\hat { j }.In the whole co-ordinate plane the force is given by F=8r3rN\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=abe=\frac { a }{ b } where a,ba,b are co-prime integers then find a×ba\times b

Details and Assumptions:

1)v0=1m/s,r0=2metre,m=1Kg{ 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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