### All Precalculus Resources

## Example Questions

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

Find the eccentricity of the following hyperbola:

**Possible Answers:**

**Correct answer:**

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:

**Possible Answers:**

**Correct answer:**

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:

**Possible Answers:**

**Correct answer:**

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:

**Possible Answers:**

**Correct answer:**

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:

**Possible Answers:**

**Correct answer:**

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:

**Possible Answers:**

**Correct answer:**

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:

**Possible Answers:**

**Correct answer:**

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:

**Possible Answers:**

**Correct answer:**

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:

**Possible Answers:**

**Correct answer:**

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:

**Possible Answers:**

**Correct answer:**

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,