Hyperbolas

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Hyperbolas

• Topic 7.5

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Definitions

• Hyperbola set of all points where the absolute
  value of the difference of the distance from any
  point on the hyperbola to the foci is contant

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Two Standard Equations

• Vertical Hyperbola
• Foci
• Vertices
• Asymptote Slopes

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Two Standard Equations

• Horizontal Hyperbola
• Foci
• Vertices
• Asymptote Slopes

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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 first term will be the positive term between
  x2 and y2
• Divide all terms by the constant

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

1. Put equation in standard form
2. Graph the center (h, k)
3. Graph the foci (look at the equation to determine
   your direction)
4. Graph the vertices
5. Graph the asymptotes (start at the center and
   use Rise over Run)
6. Draw U shapes that go through the vertices and
   stay in between the asymptotes

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Example
1) Graph Center
2) Graph Foci
3) Graph Vertices
4) Graph Asymptotes
5) Graph Hyperbola
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You Try! Write the following equation in standard
form, then graph it.