RWA#1: Unit M Concept 5: Graphing ellipses given equation

  

 Section 1:

• The set off all points, such that the sum of the distance known as the foci, is constant.
• Equation: (x-h)^2 / a^2 + (y-k)^2 / b^2=1 or (x-h)^2 / b^2 + (y-k)^2 / a^2=1 and a^2-b^2=c^2
• The key points of an ellipse are: the center, a, b, c, 2 vertices, the major axis, 2 co-vertices, the minor axis, 2 foci, and the eccentricity. To find A and B is the standard form is given A will always be the bigger number. Depending if x or y come first the graph will be either skinny or fat. If Its skinny the x value will not change from the center. to get the vertices, if its skinny the x values wont change and you will need to add and subtract whatever number a  is to find the y values. For the co-vertices the y will be the same as the center and subtract and add whatever number b is to find the x values. The major axis will depend on if its skinny or fat, if its skinny major axis will be x= whatever number x is for the center and the minor axis will equal whatever y is in the center. For a fat graph the numbers will change y will become major and x minor. To find the foci you need to know c and depending if its skinny or fat the x or y values will change from the numbers that make up the center. To find C you use  a^2-b^2 =c^2. The eccentricity will be C over A.

The closer the foci are to the vertices the ellipse will become fat and the closer they are to the center it will become more narrow or skinny.


Section 3:
A real world application that displays ellipses are earrings. Earrings can be worn on the ears and can be different material and color. Earrings can be in the form of ellipses.Most women over the world use earring. This real world application contains different sizes for ellipses.

Section 4:
http://www.mathamazement.com/Lessons/Pre-Calculus/09_Conic-Sections-and-Analytic-Geometry/ellipse.html
http://official-stardollfashion.blogspot.com/2009/06/8-hottest-trends-for-summer-2009.html