RWA#1 Unit M Concept 4-6 Graphing and Identifying Conic Sections

                                     Lets Get to Know Ellipses

1. Mathematically Definition: The set of all points such that the sum of the distance from the two points known as the foci is a constant.(Mrs. Kirch)

2.Describing the Conic Section

Algebraically:

                    

             Algebraically the equation of an ellipse will determine the fact whether it will be skinny or if it will be fat. In the equation it is easy to identify if its skinny or if it will be fat, if its skinny the number under the "x" would be greater and if it is fat then the number under the "y" would be greater. Also the "h" and "k" identify the center of the graph but once you have identified the center in the equation then you just have to switch the signs of the numbers in the "h" and "k" spots. You then also have to remember that "x" always goes with 'h" and "y" always goes with "k". then also remember that the ellipse is the one that has the plus sign inbetween the equations.

Graphically:

   

                 

         To begin to form the graph for your equation you first have to make sure that the equation is in standard form and if it inst then you have to use completing the square. Once you have completed the square and your equation is now in standard form you then continue by identifying the center (don't forget to switch the signs) and plot the point once you have identified it. You then can continue by finding the major and minor axis, the major axis would be the one that has the bigger degree on the bottom and the minor will have the smaller degree. You can continue by finding "a" and "b" those can be the square roots of the numbers on the bottom of the equation. From that you do a^2-b^2=c^2 and that will give you the c. The 2 vertices can be found depending on your major axis that number can be substituted by that number and the other number will be the difference of the center. The 2 co-vertices will have the minor number and then the difference of the numbers. For more information click here

3.Real World Application

         Ellipses are extremely common in our real world because they can be found in the earths orbit around the sun, its an ellipse because it is almost a perfect circle but not exactly which therefore makes it an ellipse. The earths eccentricity is a 0.0167 which would make it a  skinny ellipse compared to that of the orbit of Pluto which would turn out  to be 0.2488. The focus of the Earths orbit would be the sun. Since it is not the center of the orbit of the sun therefore that means that the earth can either move further away or closer throughout the orbit. For more information click here.

4. Work Cited

1. https://www.youtube.com/watch?v=5nxT6LQhXLM
2. http://www.physics.unlv.edu/~jeffery/astro/ellipse/ellipse_001.png
3. http://mathworld.wolfram.com/Ellipse.html
4. http://www.windows2universe.org/physical_science/physics/mechanics/orbit/ellipse.html
5. http://www.agt.net/public/garnold/ellipse2.gif