If the calculus are accurate, the extremes of the curve start to touch each other for some base at the right, and then the curves start running over themselves. Numerically, they seem to fit an ellipse very well.

At some point, the tips start spiraling around a dot (it cannot be seen at this zoom level).

I wonder if as the curve converges to a cardioid.

I have the result, but I do not yet know how to get it.