A circle is an ellipse with an eccentricity of zero. Both foci of that ellipse are at the same point.
In the special case of the circle, that point is called the "center".
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It is a SPECIAL form of ellipse. In an ellipse the centre and the two foci are at separate points on one axid. In a circle the centre and the two foci are ALL at the circle centre.
As the foci of an ellipse move closer together, the ellipse becomes more circular in shape. When the foci coincide, the shape is a circle. Note that circles are a subset of ellipses.
No, a conic section does not have vertices. If it is a circle, it has a center; if it is a parabola or hyperbola, it has a focus; and if it is an ellipse, it has foci.
No. Both foci are always inside the ellipse, otherwise you don't have an ellipse.
No. Both foci are always inside the ellipse, otherwise you don't have an ellipse.