Algebra 2 Graphing Hyperbolas
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It's Not Just a Bola
Graphing Hyperbolas

 

 OK, the graph of ...

 X2 + Y2 = 25

 
 is a circle, centered at (0,0) with a radius of 5 (5 2 = 25)
 

 

 
 But what do we get when we have a minus sign between the terms?
 
 I could make you build T tables and figure this out bit by bit,
 
 But hey, life is too short as it is ...
 
 So here's the deal,
 When you have a minus between the terms you get this:
 

 

 
 This is called a hyperbola.
 It kind of looks like two parabolas back to back.
 
 It is actually more like an outward reflection of the circle
 that has the same equation 
 but with a plus instead of a minus between the terms ...
 

 

 
 The lines of the hyperbola also keep getting closer and closer
 to a pair of diagonal lines.
 But they never touch or cross them.
 That makes these lines asymptotes.
 

 

 
 The slope of these asymptote lines is:
 

 

 
 Just like all the rest of this junk,
 if you put a number inside the parentheses with the X or the Y,
  it moves the center of the graph in the opposite direction.
 
 For example,

 (X + 2)2 + (Y - 3)2 = 25

 
 Everything keeps the same shape,
 but moves 3 units up and 2 units to the left:
 

 

 

   copyright 2005 Bruce Kirkpatrick

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