How do you know a star has a planet when you can see the planet?
The are several ways to discover them
1. Astrometric
2. Doppler shift but it depends on tilt
Radial velocity curves of a large variety
But a few AU ones are being found
NASA IR Space Interferometer (future)
Our solar system is only one example
Orbits have quite a variety of shapes and sizes
So far most masses are large (selection effect)
So far they are Jovian hot and cold
Preference for metal rich stars.
How do so Jupiter-type planets get close to their star?
During formation the dust disks force them to spiral inward.
Encounters and resonances move orbits and reshape them