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Advanced Algebra E-portfolio EllipsesPowerPoint Presentation

Advanced Algebra E-portfolio Ellipses

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### Advanced Algebra E-portfolioEllipses

Background

Vocabulary

Sample Problems

Calculator Hints

Sources

Feedback

Advanced algebra- 1st

Exit

Background

- Early astronomers believed that planets traveled in circular orbits, but mathematician Johannes Kepler proved that planetary orbits re actually flattened circles or ellipses.

Background

Standard Form for the equation of an ellipse with a vertical major axis:

Standard form for the equation of an ellipse with a horizontal majoraxis:

F1

F2

Vocabulary- Ellipse- The set of all points (x,y) such that the sum of the distances between (x,y) and two distinct fixed points (foci) are constant.
- Focus- The fixed points of the ellipse.

F1

F2

V

V

CV

Vocabulary- Vertices- The points on a line that pass through the foci on the major axis.
- Covertices- The endpoints of the minor axis.

F1

F2

V

V

CV

Vocabulary- Major Axis- The axis that joins two points on an ellipse farthest from its center.
- Minor Axis- The axis that joins the points on the ellipse nearest its center.

Sample Problems

- The center of the ellipse is at (0,0), and its major axis is on the y-axis. The vertices on the major axis are 4 units from the center (a=4). The vertices on the minor axis 2 units from the center (b=2). Write an equation in standard form for the ellipse.
- Step #1- Plug a and b into the equation
- X2+ y2 = 1
- 42
- Step #2 - Simplify the equation
- X2 + y2 = 1
- 4 16

Sample Problems

- Put the equation in standard form.
- 49x2 + 16y2 = 784
- Divide both sides of the equation by 784.
- Simplify:

Sample Problems

- Put the equation in standard form and find the center and vertices.
9(x2+6x+9-9) + 4(y2-2y+1-1) +49=0

9(x+3)2-81+ 4(y2-1)2-4+49=0

9(x+3)2 + 4(y-1)2=36

9(x+3)2 + 4(y-1)2 =1

36 36

(x+3)2 + (y-1)2 =1

4 9

Center (-3,1)

Vertices (-1,1)(-5,1)

(3,4)(-3,-2)

Calculator Hints

A calculator will help to simplify the equations involved in an ellipse but not graphing. There are websites that will help with graphing ellipses. All you have to do is put in the vertices and the covertices; the equation will be graphed automatically.

http://ca.geocities.com/xpf51/MATHREF/ELLIPSE.html

http://www.projects.ex.ac.uk/trol/scol/callipse.htm

http://www.1728.com/ellipse.htm

Sources

◦http://faculty.ed.umuc.edu/~swalsh/WeMathhelp/Ellipses/Solutions/Solution9.html

◦http://home.alltel.net/okrebs/pages62.html

◦http://www.pruplemath.com/modules/sqrellps.htm

Feedback

- Visually appealing, but lacking formatting consistency. Correct spelling/grammar errors.
- Clarify definitions and content to make is easier to understand. Concise presentation.

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