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Summary PRE CALCULUS - Hyperbola
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  • Pre-Calculus
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Summary notes on the topic discussions on the definition, properties, illustration, graphs, and computation about the Hyperbola. Includes sample problem and graph illustration with a suggested answers. An assessment of learning about the topic is also provided with an answer.

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Document information

  • June 19, 2023
  • 14
  • 2022/2023
  • Summary

Subjects

  • stem
  • stem 11
  • shs
  • grade 11
  • senior high school
  • calculus
  • pre calculus
  • math 11
  • hyperbola
  • graphs
  • conic section

Written for

  • Secondary school
  • Pre-Calculus
  • 4
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Hyperbola

, Hyperbola




Hyperbolas consist of two vaguely parabola shaped pieces that open either up and down or right and left. Also, just
like parabolas each of the pieces has a vertex. Note that they aren’t really parabolas, they just resemble parabolas.

There are also two lines on each graph. These lines are called asymptotes and as the graphs show as we make 𝑥
large (in both the positive and negative sense) the graph of the hyperbola gets closer and closer to the asymptotes.
The asymptotes are not officially part of the graph of the hyperbola. However, they are usually included so that we
can make sure and get the sketch correct. The point where the two asymptotes cross is called the center of the
hyperbola.

There are two standard forms of the hyperbola, one for each type shown above. Here is a table giving each form
as well as the information we can get from each one.

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