Pre-Cal 40S May 21, 2009

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Introduction to the ellipse.

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Pre-Cal 40S May 21, 2009

  1. 1. The Whisper Room What does this have to do with ellipses?
  2. 2. Generating Ellipses HOMEWORK
  3. 3. Drawing Ellipses
  4. 4. The Anatomy of The Ellipse P O O is the centre.
  5. 5. The Anatomy of The Ellipse P a a A2 A1 O O is the centre. A1A2 is the length of the major axis. It's length is 2a.
  6. 6. The Anatomy of The Ellipse P a a A2 A1 F2 O F1 O is the centre. A1A2 is the length of the major axis. It's length is 2a. PF1 & PF 2 are the focal radii of the ellipse.
  7. 7. The Anatomy of The Ellipse P a a A2 c A1 F2 O c F1 O is the centre. A1A2 is the length of the major axis. It's length is 2a. PF1 & PF 2 are the focal radii of the ellipse. OA1 = OA2 is the length of the semimajor axis with length a.
  8. 8. The Anatomy of The Ellipse B1 P b a a A2 A1 F2 O F1 b O is the centre. B2 A1A2 is the length of the major axis. It's length is 2a. PF1 & PF 2 are the focal radii of the ellipse. OA1 = OA2 is the length of the semimajor axis with length a. B1 B2 is the length of the minor axis. It's length is 2b.
  9. 9. The Anatomy of The Ellipse B1 P b a a A2 A1 F2 O F1 b O is the centre. B2 A1A2 is the length of the OB1 = OB2 is the length of the major axis. It's length is 2a. semiminor axis with length b. PF1 & PF 2 are the focal radii of the ellipse. OA1 = OA2 is the length of the semimajor axis with length a. B1 B2 is the length of the minor axis. It's length is 2b.
  10. 10. 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 OB1 = OB2 is the length of the major axis. It's length is 2a. semiminor axis with length b. 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 semimajor axis with length a. B1 B2 is the length of the minor axis. It's length is 2b.
  11. 11. 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 OB1 = OB2 is the length of the major axis. It's length is 2a. semiminor axis with length b. 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. B1 B2 is the length of the minor axis. It's length is 2b.
  12. 12. 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 OB1 = OB2 is the length of the major axis. It's length is 2a. semiminor axis with length b. 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. B1 B2 is the length of the B1 & B 2 are called the minor axis. It's length is 2b. endpoints of the minor axis.
  13. 13. ELLIPSE VERTICAL B1 b A1 a a A2 F1 c O c F2 b B2
  14. 14. 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
  15. 15. Horizontal Ellipse Vertical Ellipse
  16. 16. Generating Hyperbolas HOMEWORK

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