TITLE: Is a circle classified as an ellipse?
QUESTION [9 upvotes]: I read that an ellipse had $2$ focal points. So, I thought if a circle had $2$ points that were simply infinitesimally close together wouldn't it be classified as an ellipse?

REPLY [10 votes]: Both the foci of a circle coincide and thus, its eccentricity is zero. So yes, it is an ellipse. 
It is like that all squares are rectangles but all rectangles are not squares. 
See this link- [the most intuitive link ever seen!]
http://www.mathsisfun.com/geometry/eccentricity.html