Due to most conventional way for writing functions (two parts) that represents a ellipse is (x - a)^2 / c + (y - b)^2 / d = 1, which is similar to those of conic functions (hyperbolas) where + is replaced with - in the middle. Yet you can think of -d replaces d.
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circle and ellipse are closed curved conic section!, from bilal , Pakistan
A conic section is the intersection of a plane and a cone. By changing the angle and location of intersection, we can produce a circle, ellipse, parabola or hyperbola; or in the special case when the plane touches the vertex: a point, line or 2 intersecting lines.Traditionally, the three types of conic section are the hyperbola, the parabola, and the ellipse. The circle is a special case of the ellipse, and is of sufficient interest in its own right that it is sometimes called the fourth type of conic section.
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.
They are the shapes of the slices when you slice a cone. For example, when you slice it parallel to the base and look at the shape of the slice, you see the conic section known as a "circle". The others are the "ellipse", the "parabola", and the "hyperbola". Which one you get depends only on how you tilt the knife when you slice the cone.
Ellipse circle