Precalculus : Pre-Calculus

Study concepts, example questions & explanations for Precalculus

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Example Questions

Example Question #97 : Hyperbolas And Ellipses

Find the eccentricity of the hyperbola with the following equation:

Possible Answers:

Correct answer:

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 #98 : Hyperbolas And Ellipses

Find the eccentricity of the following hyperbola:

Possible Answers:

Correct answer:

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 #99 : Hyperbolas And Ellipses

Find the eccentricity of the following hyperbola:

Possible Answers:

Correct answer:

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 #100 : Hyperbolas And Ellipses

Find the eccentricity of the following hyperbola:

Possible Answers:

Correct answer:

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 #191 : Conic Sections

Find the eccentricity of the following hyperbola:

Possible Answers:

Correct answer:

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 #191 : Conic Sections

Find the eccentricty of the following hyperbola:

Possible Answers:

Correct answer:

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 #103 : Hyperbolas And Ellipses

Find the eccentricity of the following hyperbola:

Possible Answers:

Correct answer:

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 #104 : Hyperbolas And Ellipses

Find the eccentricity of the following hyperbola:

Possible Answers:

Correct answer:

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 #105 : Hyperbolas And Ellipses

Find the eccentricity of the following hyperbola:

Possible Answers:

Correct answer:

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 #106 : Hyperbolas And Ellipses

Find the eccentricity for the following hyperbola:

Possible Answers:

Correct answer:

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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