Working With Hyperbolas
        (you have to know where to look)




urban geometry hyperbolas by flickr user johncarney
The Standard Form for the Equation of a Hyperbola

       Horizontal Orientation             Vertical Orientation




    ...
The Anatomy of The Hyperbola                  P

                                B1
                               b   c F...
Horizontal Hyperbola   Vertical Hyperbola




      a b                           a
        O
                            ...
The Pythagorean Property


                       B1
                       b a c
                              F1
       ...
Conics Animations Source




http://mathdemos.gcsu.edu/mathdemos/family_of_functions/conic_gallery.html
For the hyperbola whose equation is given below.
      (i) Write the equation in standard form
      (ii) Determine the le...
For the hyperbola whose equation is given below.
      (i) Write the equation in standard form
      (ii) Determine the le...
Upcoming SlideShare
Loading in...5
×

Pre-Cal 40S Slides May 16, 2008

1,425

Published on

More on working with the hyperbola.

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

  • Be the first to like this

No Downloads
Views
Total Views
1,425
On Slideshare
0
From Embeds
0
Number of Embeds
6
Actions
Shares
0
Downloads
7
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

Pre-Cal 40S Slides May 16, 2008

  1. 1. Working With Hyperbolas (you have to know where to look) urban geometry hyperbolas by flickr user johncarney
  2. 2. The Standard Form for the Equation of a Hyperbola Horizontal Orientation Vertical Orientation Differences Similarities • numerators have different • have the same terms orientation • both equal 1 • numerators have • both are differences opposite signs • both have same denominators • both have square binomials • (h, k) indicates center
  3. 3. The Anatomy of The Hyperbola P B1 b c F F2 a 1 A 1 O c A2 B2 O is the centre, it has coordinates (h, k). A1A2 is the length of the B1 B2 is the length of the transverse axis. It's length is 2a. conjugate axis. It's length is 2b. PF1 & PF 2 are the focal F 1 & F 2 are called the foci. They radii of the hyperbola. are c units from the centre. OA1 = OA2 is the length of the A1 & A 2 are called the semitransverse axis with length a. vertices of the hyperbola. OB1 = OB2 is the length of the B 1 & B 2 are called the endpoints semiconjugate axis with length b. of the conjugate axis.
  4. 4. Horizontal Hyperbola Vertical Hyperbola a b a O O b
  5. 5. The Pythagorean Property B1 b a c F1 F2 A2 O c A 1 B2 2 2 2 c = a +b Horizontal Hyperbola Vertical Hyperbola
  6. 6. Conics Animations Source http://mathdemos.gcsu.edu/mathdemos/family_of_functions/conic_gallery.html
  7. 7. For the hyperbola whose equation is given below. (i) Write the equation in standard form (ii) Determine the lengths of the transverse and conjugate axes, the coordinates of the verticies and foci, and the equations of the asymptotes. (iii) Sketch a graph of the hyperbola.
  8. 8. For the hyperbola whose equation is given below. (i) Write the equation in standard form (ii) Determine the lengths of the transverse and conjugate axes, the coordinates of the verticies and foci, and the equations of the asymptotes. (iii) Sketch a graph of the hyperbola. SLOPE INTERCEPT FORM
  1. A particular slide catching your eye?

    Clipping is a handy way to collect important slides you want to go back to later.

×