RWA# 1: Unit M Concept 4-6 : Conic sections in real life

Ellipses

1) The mathematical definition of an ellipse is, "The set of all points, such that the sum of the distance from 2 points known as the oci, is a constant." -Mrs. Kirch

2) An ellipse includes the center, major and minor axis, 2 verticies, 2 co-verticies, 2 foci and and eccentricity along with a, b and c.

Here is what the equation of an ellipse looks like: 

(http://www.descarta2d.com/BookHTML/Chapters/ell.html)

Here is how an ellipse looks like graphically: 

(http://www.mathwarehouse.com/ellipse/equation-of-ellipse.php) 

We can automatically tell how our graph is going to look like graphically when the equation is given. We can tell if the ellipse is "fat" when the biggest number comes first(under x) and the ellipse will be skinny if the bigger number is under y. We can also figure out the center by using (x,y) and plugging it into (h,k) when x goes with h, and y goes with k. Both verticies will be the same number away from the center, along with the co-verticies and the 2 foci. 

To figure out how the equation will graph, we must find some "hints" that can lead to other answers. First, once the equation is given, we can find out the center, which is (h,k). After finding out the center, we can find out "a" and "b". The square root of "a" will always be the bigger number when dealing with ellipses and the smaller number will be "b". To figure out c, we can use "a^2-b^2=c^2. Once c is found, we can find the eccentricity which would be "c/a". The eccentricity of an ellipse is between 0 to 1. The verticies, co-verticies, foci, major and minor axis depend on whether the bigger number is under x or y.  

For further explanation, refer to the video below. 

3) Below, there is a picture of a soccer/track field in the shape of an ellipse. The midpoint would be the point in the middle which separates the middle of the field. The major axis would go horizontally, and the minor axis would go vertically. In this case, algebraically, the bigger number would come first, under x.

(https://www.google.com/search?q=racetrack&safe=active&client=firefox-a&hs=hai&rls=org.mozilla:en-US:official&source=lnms&tbm=isch&sa=X&ei=46r6UsiUH6O92wW4poC4Cw&ved=0CAoQ_AUoAg&biw=1280&bih=647#facrc=_&imgdii=_&imgrc=bWTXj9M8I81LGM%253A%3BV553ddJQAu7xVM%3Bhttp%253A%252F%252Fus.123rf.com%252F400wm%252F400%252F400%252Fexperimental%252Fexperimental1001%252Fexperimental100100014%252F6252442-football-soccer-field-pitch-vector-along-with-racetrack.jpg%3Bhttp%253A%252F%252Fwww.123rf.com%252Fphoto_6252442_football-soccer-field-pitch-vector-along-with-racetrack.html%3B1200%3B936)

4) Work Cited: 

(http://www.descarta2d.com/BookHTML/Chapters/ell.html)

 (http://www.mathwarehouse.com/ellipse/equation-of-ellipse.php)

((https://www.google.com/search?q=racetrack&safe=active&client=firefox-a&hs=hai&rls=org.mozilla:en-US:official&source=lnms&tbm=isch&sa=X&ei=46r6UsiUH6O92wW4poC4Cw&ved=0CAoQ_AUoAg&biw=1280&bih=647#facrc=_&imgdii=_&imgrc=bWTXj9M8I81LGM%253A%3BV553ddJQAu7xVM%3Bhttp%253A%252F%252Fus.123rf.com%252F400wm%252F400%252F400%252Fexperimental%252Fexperimental1001%252Fexperimental100100014%252F6252442-football-soccer-field-pitch-vector-along-with-racetrack.jpg%3Bhttp%253A%252F%252Fwww.123rf.com%252Fphoto_6252442_football-soccer-field-pitch-vector-along-with-racetrack.html%3B1200%3B936)
https://www.youtube.com/watch?v=5nxT6LQhXLM