Conic section

A curve formed by intersecting a plane with a double cone. Its nondegenerate forms are circles, ellipses, parabolas, and hyperbolas; special intersections produce degenerate cases.

Cone: A three-dimensional surface or solid with a circular or polygonal base narrowing to an apex. A double cone is the surface being cut to form a conic section.
Conic section classification: The classification of second-degree plane curves by their geometry or equation coefficients. It distinguishes ellipses, parabolas, hyperbolas, and degenerate cases.
Circle: The set of points in a plane at a fixed distance from one center. A plane perpendicular to the cone’s axis can cut a circular section.
Kepler's laws of planetary motion: Three laws describing how planets orbit the Sun, including their motion along ellipses. The first law identifies planetary orbits as ellipses with the Sun at one focus.
Menaechmus: An ancient Greek mathematician associated with the discovery of conic sections. He studied curves formed by cutting cones, reportedly to solve the Delian problem.
Plane: A flat two-dimensional surface extending indefinitely in three-dimensional space. The plane’s orientation relative to the cone determines the resulting curve.
Eccentricity (mathematics): A parameter measuring how much a conic differs from a circle. Its value separates circles, ellipses, parabolas, and hyperbolas.
Ellipse: A closed plane curve whose points have a constant sum of distances from two foci. An oblique plane cutting one nappe usually produces an ellipse.
Projectile motion: The motion of an object launched into the air under gravity and other forces. In an ideal uniform gravitational field, a projectile follows a parabolic path.
Apollonius of Perga: A Greek mathematician whose treatise Conics developed the systematic theory of conic sections. His work named and organized the principal conic curves.

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