What is the name of this "ellipse"?

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When I was in school, I learned what a circle was. Later, I learned what an ellipsis was. I also discovered that a circle is a particular case of ellipse (both foci at the same location).

Now, I'm pretty sure mathematicians have already studied "generalized ellipsis". I mean ellipses with more than two foci.

What's the name of these mathematical objects?

Some links to studies of these objects will be much appreciated.