Derive the Equation of a Hyperbola from the Foci

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question 1 of 3

Which of the following is the shape of a hyperbola?

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1. What is the definition of a hyperbola?

2. What is the equation of a hyperbola with a horizontal transverse axis such that (h, k) is its center, a is the distance from the center to a vertex, c is the distance from the center to the foci, and b2 = c2 - a2?

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About This Quiz & Worksheet

This study assessment will cover in detail how to derive the equation of a hyperbola from the foci. Use the quiz to answer questions on topics like the shape of a hyperbola and its proper definition.

Quiz & Worksheet Goals

Use the quiz and worksheet to:

  • Solve an equation of a hyperbola with a horizontal transverse axis
  • Find a specific variable in a problem where you're given the center of a hyperbola and necessary distances
  • Identify the equation of a hyperbola when you're given the center of its axis and the distance to its vertex and foci

Skills Practiced

  • Problem solving - use acquired knowledge to solve practice problems that involve deriving the equation of a hyperbola from the foci
  • Critical thinking - apply relevant concepts to examine information about hyperbolas in a different light
  • Information recall - access the knowledge you've gained regarding the horizontal transverse axis
  • Making connections - use understanding of the concept of a hyperbola equation and how it's connected to the foci

Additional Learning

Use the lesson called Derive the Equation of a Hyperbola from the Foci for more on the subsequent study topics:

  • The shape of a butterfly as an example of a hyperbola
  • Graphing a hyperbola
  • A hyperbola's mathematical characteristics
  • The midpoint formula
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