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Hyperbola - Finding the Equation - PowerPoint PPT Presentation


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Horizontal Axis. Vertical Axis. Hyperbola - Finding the Equation. Recall that the equations for the hyperbola are given by . Hyperbola - Finding the Equation. Summary of meanings of the constants:. The center is at C(h, k) .

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Presentation Transcript
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Horizontal Axis

Vertical Axis

Hyperbola - Finding the Equation

  • Recall that the equations for the hyperbola are given by ...
slide2

Hyperbola - Finding the Equation

  • Summary of meanings of the constants:

The center is at C(h, k).

The vertices are a units from the center on the transverse axis.

The foci are c units from the center on the transverse axis.

The values of a, b, and c are related by the equation ...

Slide 2

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Hyperbola - Finding the Equation

  • Example 1:
  • Find the equation of the hyperbola with the given
  • vertices and foci ...
  • The first step is to plot these points on a coordinate plane.

Slide 3

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Hyperbola - Finding the Equation

  • The center will be the midpoint of the line segment joining the vertices (also the foci) ...
  • The distance from the center to a vertex is a = 4.
  • The distance from the center to a focus is c = 6.

Slide 4

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Hyperbola - Finding the Equation

  • Using the formula ...

the value of b can be found.

Slide 5

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Hyperbola - Finding the Equation

  • Summary:
  • Since the vertices are vertical, the hyperbola has a vertical axis ...

and the equation is ...

Slide 6

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Hyperbola - Finding the Equation

  • Example 2:
  • Find the standard form of the hyperbola given by ...
  • Solution:

Slide 7

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Hyperbola - Finding the Equation

  • The standard form of the hyperbola is ...

Slide 8

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Hyperbola - Finding the Equation

END OF PRESENTATION

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