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There are two points: the foci.
focus
No there can never be a single point. But yes there are two such points called foci( each called focus) that helps to define an ellipse. An ellipse can then be defined as a curve which is actually the locus of all points in a plane,the sum of whose distances from two fixed points (the foci) is a given(positive)constant . This is further expressed mathematically to obtain the equation of an ellipse.
An ellipse is a shape on which the sum of the distances from every point to two points inside called the foci (focuses) is always the same number. A circle is an ellipse with both foci (focuses) at the same point.