Hyperbolas

1
Hyperbolas

• Ch 7.5

2
Two Standard Equations

• Vertical Hyperbola
• Vertices
• Asymptote Slopes

• Horizontal Hyperbola
• Vertices
• Asymptote Slopes

3
Writing in Standard Form

• Complete the square for both the x-terms and
  y-terms and move the constant to the other side
  of the equation
• The front term will be the positive term between
  x2 and y2
• Divide all terms by the constant and simplify

4
Example
Group terms
Complete the square
Simplify
Dont forget the negative nine!
Divide by Constant
5
Graphing the hyperbola

• Put equation in standard form
• Graph the center (h, k)
• Graph the vertices
• Graph the asymptotes (start at the center and
  use Rise over Run)
• Draw U shapes that go through the vertices and
  stay in between the asymptotes

6
Example
1) Graph Center
2) Graph Vertices
3) Graph Asymptotes
4) Graph Hyperbola