RWA1: Unit M Concepts 4-6 - Conic Sections in real life.

http://www.youtube.com/watch?v=lvAYFUIEpFI

http://www.mathsisfun.com/geometry/ellipse.html

1. An ellipse is the set of all points on a plane whose distance from two points add up to be a constant

2. The equation algebraically is (x-h)^2/a^2+(y-k)^2/b^2=1

     An ellipse is almost like a smashed circle. (as shown above)

     To find the standard form we must use the center point of the ellipse and plug it into the equation.(x,y)=(h,k). If the ellipse is skinny a^2 goes under y and if its fat a^2 goes under x. the major axis is the longest diameter of the ellipse and the minor axis is the shortest. To find a you would find the number from one of the vertices to the center of the ellipse. To find b you would find the distance from one of the covertices to the center. To find c we would have to use a^2-b^2=c^2. To find the eccentricity we put c over a and it should be less than 1. If you place the foci farther away from the center the wider the ellipse will get. 

3. Conic sections are used everyday in the real world. They may not seem huge but they make an important difference. One example is with tanks that carry heating oil or gasoline. The tanks are never circular but rather elliptical. "This gives them a high capacity, but with a lower center-of-gravity, so that they are more stable when being transported." (http://mathforum.org/library/drmath/view/62576.html) If the tank was a circle then its height would be greater and it wouldn't fit under bridges. Without an elliptical tank things like oil and gasoline would be much harder to transport.

     These conic sections also get things going such as bicycles. The gear that connects to the pedal crank is basically an elliptical shape. "Here the difference between the major and minor

  axes of the ellipse is used to account for differences in the speed and force applied"(http://mathforum.org/library/drmath/view/62576.html)

With this elliptical shape your legs are able to push and pull more effectively. Conic sections are used everyday in the real world with things that are the least noticeable yet make the biggest differences. A world without conic sections would be difficult.

4. References:

. http://mathforum.org/library/drmath/view/62576.html

. http://www.mathsisfun.com/geometry/ellipse.html

. http://www.youtube.com/watch?v=lvAYFUIEpFI

. http://www.mathopenref.com/ellipseaxes.html

. http://www.mathopenref.com/ellipsefoci.html