Conic Section

A coinc section is the 1D curve obtained from intersecting a 2D plane with a 3D cone. The four types are: circle, ellipse, parabola, hyperbola.

Circle
A circle is a rotatope with no flat dimensions and two round dimensions. It is, therefore, the 2D hypersphere. It can also be considered as the set of all points that are the same distance from a point (the center of a circle) in the plane.

Ellipse
An ellipse is in the form of this formula: $$\frac{{x}^{2}}{{a}^{2}} + \frac{{y}^{2}}{{b}^{2}} = 1$$

Parabola
A parabola is a conic section with an eccentricity equal to one. All quadratic curves are also parabolas.

Hyperbola
A hyperbola is a conic section with an eccentricity of greater than one. The general equation of a hyperbola is $$\frac{{x}^{2}}{{a}^{2}} - \frac{{y}^{2}}{{b}^{2}} = 1$$.