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### Conic Sections An Introduction to Conic Sections - Analytic Geometry

The Greeks discovered the properties that define conics in terms of points and lines. These properties are important tool for current day problems with the behaviors of atoms, molecules and outer space. Particles that move under the influence of an inverse square force field has a path that is described by conic sections.

 Conic Section Definition Circle Each of the geometric figures are obtained by intersecting a double-napped right circular cone with a plane. Thus, the figures are called conic sections or conics. If the plane cuts completely across one nappe of the cone and is perpendicular to the axis of the cone, the curve of the section is called a circle. Ellipse If the plane isn't perpendicular to the axis of the cone, it is called an ellipse. An ellipse is the set of all points in a plane, the sum of the distances from two fixed points in the plane is constant. Many comets have elliptical orbits. Parabola If the plane doesn't cut across one entire nappe or intersect both nappes, the curve of the intersection is called a parabola. A parabola is the set of all points in a plane equidistant from a fixed point and a fixed line in the plane. Hyperbola If the plane cuts through both nappes of the cone, the curve is called a hyperbola. The hyperbola is the set of all points in a plane. The difference of whose distance from two fixed points in the plane is the positive constant.

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