Elliptical orbit in the presence of a centripetal force that is proportional to the distance to the center of rotation.
The parametric equation is as follows:

${\displaystyle x=a*\cos \omega }$

${\displaystyle y=b*\sin \omega }$

This can also be written as follows, showing that the elliptical motion with that particular velocity profile can be seen as a vector addition of two uniform circular motions:

${\displaystyle x=({\frac {a+b}{2}})\cos \omega +({\frac {a-b}{2}})\cos \omega }$

${\displaystyle y=({\frac {a+b}{2}})\sin \omega -({\frac {a-b}{2}})\sin \omega }$