# Precalculus : Find the Eccentricity of a Hyperbola

## Example Questions

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### Example Question #1 : Find The Eccentricity Of A Hyperbola

Find the eccentricity of the following hyperbola:

Explanation:

In order to find the eccentricity of , first determine the values of  and  from the standard form of the hyperbola:

Use the following formula to calculate eccentricity.  The eccentricity of a hyperbola should always be greater than 1.

Substitute and solve for eccentricity.

### Example Question #1 : Find The Eccentricity Of A Hyperbola

Find the eccentricity of the hyperbola with the following equation:

Explanation:

Recall the standard form of the equation of a horizontal hyperbola:

, where  is the center.

For a horizontal hyperbola, use the following equation to find the eccentricity:

, where

For the given hyperbola,

and

Thus,

### Example Question #3 : Find The Eccentricity Of A Hyperbola

Find the eccentricity of the following hyperbola:

Explanation:

Recall the standard form of the equation of a horizontal hyperbola:

, where  is the center

For a horizontal hyperbola, use the following equation to find the eccentricity:

, where

For the given hyperbola,

and

Thus,

### Example Question #2 : Find The Eccentricity Of A Hyperbola

Find the eccentricity of the following hyperbola:

Explanation:

Recall the standard form of the equation of a horizontal hyperbola:

, where  is the center

For a horizontal hyperbola, use the following equation to find the eccentricity:

, where

For the given hyperbola,

and

Thus,

### Example Question #5 : Find The Eccentricity Of A Hyperbola

Find the eccentricity of the following hyperbola:

Explanation:

Recall the standard form of the equation of a horizontal hyperbola:

, where  is the center

For a horizontal hyperbola, use the following equation to find the eccentricity:

, where

For the given hyperbola,

and

Thus,

### Example Question #6 : Find The Eccentricity Of A Hyperbola

Find the eccentricity of the following hyperbola:

Explanation:

Recall the standard form of the equation of a horizontal hyperbola:

, where  is the center

For a horizontal hyperbola, use the following equation to find the eccentricity:

, where

For the given hyperbola,

and

Thus,

### Example Question #7 : Find The Eccentricity Of A Hyperbola

Find the eccentricty of the following hyperbola:

Explanation:

Recall the standard form of the equation of a horizontal hyperbola:

, where  is the center

Start by putting the given equation into the standard form of the equation of a horizontal hyperbola.

Group the  terms and  terms together.

Factor out  from the  terms and  from the  terms.

Complete the squares. Remember to add the same number on both sides!

Divide both sides by .

Factor both terms to get the standard equation.

For a horizontal hyperbola, use the following equation to find the eccentricity:

, where

For the given hyperbola,

and

Thus,

### Example Question #1 : Find The Eccentricity Of A Hyperbola

Find the eccentricity of the following hyperbola:

Explanation:

Recall the standard form of the equation of a vertical hyperbola:

, where  is the center

For a horizontal hyperbola, use the following equation to find the eccentricity:

, where

For the given hyperbola,

and

Thus,

### Example Question #1 : Find The Eccentricity Of A Hyperbola

Find the eccentricity of the following hyperbola:

Explanation:

Recall the standard form of the equation of a vertical hyperbola:

, where  is the center

For a horizontal hyperbola, use the following equation to find the eccentricity:

, where

For the given hyperbola,

and

Thus,

### Example Question #31 : Hyperbolas

Find the eccentricity of the following hyperbola:

Explanation:

Recall the standard form of the equation of a vertical hyperbola:

, where  is the center

For a horizontal hyperbola, use the following equation to find the eccentricity:

, where

For the given hyperbola,

and

Thus,

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