Calculate foci of planetary orbit given known parameters

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Main Question or Discussion Point

Hello everyone. I am trying to calculate the focal points of the ellipse traced by a planet in orbit around a star, given the following known parameters:
  • [itex]M_{sun}[/itex] Mass of the sun
  • [itex]r_{planet}[/itex] Position vector of the planet from the sun
  • [itex]m_{planet}[/itex] Mass of the planet
  • [itex]v_{planet}[/itex] Velocity of the planet
  • [itex]G[/itex] Gravitational constant
  • [itex]F_{grav} = G\frac{Mm}{r^{2}}[/itex]

I would like to find (if possible) the orbital information of the planet (including eccentricity, focal points, and axes, if possible) based on these pieces of data. Is it possible to calculate the focal points of its orbit based on these parameters? If more parameters are necessary, I might be able to add them. Any help would be greatly appreciated! (The focal points of an ellipse are shown below.)

256px-Ellipse_with_focus.svg.png
 
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