Lesson #154 Hyperbolas

  
Quote of the Day:
"When you are courting a nice girl an hour seems like a 
   second.  When you sit on a red-hot cinder a second seems 
   like an hour.  That's relativity."  -- Albert Einstein

Objectives:
The student will analyze given hyperbolas.
The student will write the equation for an hyperbola given
   certain information.

1. Definition of an Hyperbola:
   An hyperbola is the set of points in a plane whose
   distances from two fixed points have a constant 
   difference.
    

2. Distribute a copy of the Hyperbola paper to each 
   student.  Have each student trace out an hyperbola while 
   I do one at the overhead.  The purpose of this is to 
   have students understand the definition of the hyperbola
   by locating points which satisfy the definition.

        Hyperbola Paper

3. Develop the equation for an hyperbola with center at the 
   origin, foci at (-c, 0) and (c, 0), and constant 
   difference equal to 2a.

    
    Given foci are (-c, 0) and (c, 0)
    Let the constant difference = 2a 


       

       
4. The general forms for an hyperbola are:

       

       

5. Examples:

       

       

       

6. Assignment:
   Finish Hyperbola Paper
   p. 739 (15a, 16a,b, 17b, 20a, 33a, 34b, 35b, 50)   

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