Pre-Cal 40S Slides May 13, 2008

607 views

Published on

Working with the ellipse.

Published in: Education, Business
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
607
On SlideShare
0
From Embeds
0
Number of Embeds
26
Actions
Shares
0
Downloads
8
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

Pre-Cal 40S Slides May 13, 2008

  1. 1. The Whisper Room What does this have to do with ellipses?
  2. 2. The Anatomy of The Ellipse B1 P b a a A2 c A1 F2 O c F1 b O is the centre. B2 A1A2 is the length of the B1 B2 is the length of the major axis. It's length is 2a. minor axis. It's length is 2b. PF1 & PF 2 are the focal F 1 & F 2 are called the foci. They radii of the ellipse. are c units from the centre. OA1 = OA2 is the length of the A1 & A 2 are called the semimajor axis with length a. vertices of the ellipse. OB1 = OB2 is the length of the B1 & B 2 are called the semiminor axis with length b. endpoints of the minor axis.
  3. 3. ELLIPSE VERTICAL B1 b a a A2 c A1 F2 O c F1 b B2
  4. 4. Horizontal Ellipse Vertical Ellipse
  5. 5. The Pythagorean Property B1 a b A2 a A1 F2 c F1 b 2 2 b+ c = a2 B 2 2 2 c =a - b Horizontal Ellipse Vertical Ellipse
  6. 6. FOCAL RADII PROPERTY Constant BY SYMMETRY
  7. 7. Sketch each ellipse. Identify the length of the major and minor axes, the coordinates of the center, foci and vertices.
  8. 8. Sketch each ellipse. Identify the length of the major and minor axes, the coordinates of the center, foci and vertices.
  9. 9. From Standard to General Form and Back Again ... Standard Form General Form Standard Form

×