The common collector colpitts oscillator is not what you have drawn. It is like this: -

[![enter image description here][1]][1]

And here is a document I wrote that derives the oscillation frequency and talks about the capacitor ratio: -

[![enter image description here][2]][2]


  [1]: https://i.sstatic.net/OuKNL.jpg
  [2]: https://i.sstatic.net/HJPwN.png