One thing Conic is useful for is creating an elliptical arc segment that is tangent to two lines.

Here is a stylized bug that is created from 3 conics and their tangent lines.

While not elaborate or even very useful, this was a very quick way to demonstrate the Conic in actual use.

I created lines to be used as guides for the Conic and Joined the resulting conic segment to the original guide lines.

I offset the conic segments .1mm to emphasize them for the image capture.

I was pleased to learn that Conics seem to result in a nice organic flow.