Hyperbola - Finding the Equation

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# Hyperbola - Finding the Equation - PowerPoint PPT Presentation

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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## Hyperbola - Finding the Equation

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Presentation Transcript

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).

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

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

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

Hyperbola - Finding the Equation

• Using the formula ...

the value of b can be found.

Slide 5

Hyperbola - Finding the Equation

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

and the equation is ...

Slide 6

Hyperbola - Finding the Equation

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

Slide 7

Hyperbola - Finding the Equation

• The standard form of the hyperbola is ...

Slide 8

Hyperbola - Finding the Equation

END OF PRESENTATION

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