CONIC SECTIONS AND ITS APPLICATIONS
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This document defines and provides examples of different types of conic sections - parabolas, ellipses, and hyperbolas. It explains that conic sections are curves formed by the intersection of a plane with a cone, and that points on a conic section have a fixed ratio between their distance to a focus point and its directrix line, known as eccentricity. Eccentricity values distinguish the different conic section types. Examples of each in diagrams and applications like planetary orbits, bicycle gears, and network synchronization are also provided.
CONIC SECTIONS AND ITS APPLICATIONS
- 2. a conic section (or just conic) is a curve obtained as the intersection of a cone with a plane.
- 3. PARABOLA ELLIPSE HYPERBOLA
- 4. FOCUS DIRECTRIX ECCENTRICITY
- 5. a conic consists of those points whose distances to some point, called a Focus, and some line, called a Directrix, are in a fixed ratio, called the Eccentricity. F1, F2, F3 - FOCUS
- 6. The eccentricity of an ellipse is greater than zero but less than 1. The eccentricity of a parabola is 1. The eccentricity of a hyperbola is greater than 1.
- 7. A parabola is approximately U- shaped when oriented as shown in the diagram, but which can be in any orientation in its plane.
- 8. trajectory of a particle or body in motion under the influence of a uniform gravitational field.
- 9. THE VOMIT COMET
- 11. “ The orbits along which the planets travel around the Sun are ellipses with the Sun at one focus ” - JOHN KEPPLER
- 12. In bicycles, two elliptical gears may be used for mechanical advantage to produce variable angular speed or torque.
- 13. A hyperbola has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows. If the plane intersects both halves of the double cone but does not pass through the apex of the cones then the conic is a hyperbola.
- 14. Developing a Reference Model for Networked Flexible Work through Industry Trials The Hyperbola of Synchronization
- 15. BY JAFFER SHERIFF M