Advanced Algebra E-portfolio Ellipses

1
Advanced Algebra E-portfolioEllipses
Background
Vocabulary
Sample Problems
Calculator Hints
Sources
Feedback
Advanced algebra- 1st
Exit
2
Background

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

3
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 major axis
4
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.

5
Vocabulary

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

6
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.

7
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 (a4).
  The vertices on the minor axis 2 units from the
  center (b2). 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

8
Sample Problems

• Put the equation in standard form.
• 49x2 16y2 784
• Divide both sides of the equation by 784.
• Simplify

9
Sample Problems

• Put the equation in standard form and find the
  center and vertices.
• 9(x26x9-9) 4(y2-2y1-1) 490
• 9(x3)2-81 4(y2-1)2-4490
• 9(x3)2 4(y-1)236
• 9(x3)2 4(y-1)2 1
• 36 36
• (x3)2 (y-1)2 1
• 4 9
• 
  Center (-3,1)
• 
  Vertices (-1,1)(-5,1)
• (3,4)(-3,-2)

10
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/xpf
51/MATHREF/ELLIPSE.html http//www.projects.ex.ac.
uk/trol/scol/callipse.htm http//www.1728.com/elli
pse.htm
11
Sources
?http//faculty.ed.umuc.edu/swalsh/WeMathhelp/Ell
ipses/Solutions/Solution9.html ?http//home.alltel
.net/okrebs/pages62.html ?http//www.pruplemath.co
m/modules/sqrellps.htm
12
Feedback

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