Pre-Cal 40S May 21, 2009
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Pre-Cal 40S May 21, 2009

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Introduction to the ellipse.

Introduction to the ellipse.

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Pre-Cal 40S May 21, 2009 Pre-Cal 40S May 21, 2009 Presentation Transcript

  • The Whisper Room What does this have to do with ellipses?
  • Generating Ellipses HOMEWORK
  • Drawing Ellipses
  • The Anatomy of The Ellipse P O O is the centre.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • ELLIPSE VERTICAL B1 b A1 a a A2 F1 c O c F2 b B2
  • 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
  • Horizontal Ellipse Vertical Ellipse
  • Generating Hyperbolas HOMEWORK