CONIC SECTIONS AND ITS APPLICATIONS

CONIC SECTIONS AND ITS REAL LIFE APPLICATIONS

1. CONICS

2. Conic Sections a conic section (or just conic ) is a curve obtained as the intersection of a cone with a plane .

3. TYPES OF CONIC SECTIONS PARABOLA ELLIPSE HYPERBOLA

4. THREE DEFINING CONDITIONS FOCUS DIRECTRIX ECCENTRICITY

5. FOCUS AND DIRECTRIX a conic consists of those points whose distances to some point, called a Focus , and some line, called a D irectrix , are in a fixed ratio, called the Eccentricity . F1, F2, F3 - FOCUS

6. ECCENTRICITY 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. PARABOLA A parabola is approximately U-shaped when oriented as shown in the diagram , but which can be in any orientation in its plane.

8. APPLICATIONS trajectory of a particle or body in motion under the influence of a uniform gravitational field.

9. APPLICATIONS THE VOMIT COMET

10. ELLIPSE

11. APPLICATIONS “ The orbits along which the planets travel around the Sun are ellipses with the Sun at one focus ” - JOHN KEPPLER

12. APPLICATION In bicycles, two elliptical gears may be used for mechanical advantage to produce variable angular speed or torque.

13. HYPERBOLA 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. APPLICATIONS Developing a Reference Model for Networked Flexible Work through Industry Trials The Hyperbola of Synchronization

15. THANK YOU !! BY JAFFER SHERIFF M

16. http://en.wikipedia.org http:// cordis.europa.eu Google Images REFERENCES