RWA #1: Unit M Concept 5 (graphing and identifying all parts of an Ellipse)

1. The mathematical definition of an ellipse is "the set of all points such that the sum of the distance from two points is a constant."
-Crystal Kirch
2. Algebraically, the equation of an ellipse may look like this:

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&docid=DPKcpdDOYy4itM&tbnid=w0dDhRwnk-AOBM:&ved=0CAUQjRw&url=http%3A%2F%2Fwww.mathwarehouse.com%2Fellipse%2Fequation-of-ellipse.php&ei=vdX6UvLvKs2xqwGvhoAI&bvm=bv.61190604,d.b2I&psig=AFQjCNGfO6poWHy-sP11pQ6Htlr3jjQt6w&ust=1392256786266063
With this equation alone, the center can always be found. The "h and k" are always with the  X and Y terms. If the X and Y squared terms are alone without being in parenthesis it simply means that they are both zero, for example "x^2/4 + (y-4)^2/16," the X term is being simplified or otherwise may be re-written as "(x + 0)^2/4." To find the vertices we would need to look at the bottom portions of the term fractions, generally these would be referred to as "a^2" and "b^2." We can easily tell which is the a because with an ellipse, the A is always bigger than B. If the A is under the X then the Y of the vertices would not change. This would also be associated as the major axis line. If the A was under the Y then it would be the X of the vertices that wouldn't change and then the X be associated (in linear form) as the major axis. The vertices, major axis, and foci will always have this one digit in common, depending on the placement of the A. Along with finding A, we've also found B- together they can be plugged into the a^2 -b^2 = c^2 to get C. With the C we can finish the other half of the foci.

Another way to describe an ellipse is graphically. By having the equation in standard form, which has both terms squared and equal to one, we can infer whether the graph will be "skinny" by having the a under the Y or "fat." by having the a under the X. In other words, if the longer distance is along the x-axis then it would be a horizontal ellipse therefore can be called "fat," now if the longer square root distance goes along the Y-axis then it would be vertical, therefore can be called "skinny."

3. A real life example of an ellipse I found was a race/running track with "designs that help designers take into account top speeds and such depending on shape." According to this website: http://www.barrington220.org/cms/lib2/IL01001296/Centricity/Domain/112/conics%20review%20word%20problemsP2.pdf, the extended circular form of the track. Inside the ellipse are the two  points that are like the foci on the track.

Another thing I found out is that you can use a runner running along the track to find some of its portions. The runner acts as a point on the ellipse because they touch the actual track. If the runner's circling is further away, we can infer that they are currently long the major axis, which as we already know, the longer constant distance that decides the shape of the ellipse.

Please refer to the video below for any further questions:
http://youtu.be/6pDh42E2bbA

4. - http://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&docid=DPKcpdDOYy4itM&tbnid=w0dDhRwnk-AOBM:&ved=0CAUQjRw&url=http%3A%2F%2Fwww.mathwarehouse.com%2Fellipse%2Fequation-of-ellipse.php&ei=vdX6UvLvKs2xqwGvhoAI&bvm=bv.61190604,d.b2I&psig=AFQjCNGfO6poWHy-sP11pQ6Htlr3jjQt6w&ust=1392256786266063
-http://www.barrington220.org/cms/lib2/IL01001296/Centricity/Domain/112/conics%20review%20word%20problemsP2.pdf
-http://youtu.be/6pDh42E2bbA