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Circles, parabolas, ellipses, and hyperbolas are all conic sections. Out of these conic sections, the circle and ellipse are the ones which define a closed curve.
Ellipse circle
A conic section is a curve formed by the intersection of a plane with a cone (conical surface). If the section is parallel to the base of the cone, the conic section has a fixed diameter and is a circle. Any other plane that does not intersect the apex is either a parabola, a hyperbola, or an ellipse.
The hyperbola is the curve at the boundary of the intersection of the conewith a cutting plane parallel to the cone's axis.
Those are known as conic section, and they are described by equations of degree 2.