Precalculus : Hyperbolas

Study concepts, example questions & explanations for Precalculus

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Example Questions

Example Question #1 : Hyperbolas

Using the information below, determine the equation of the hyperbola.

Foci:  and 

Eccentricity: 

Possible Answers:

Correct answer:

Explanation:

General Information for Hyperbola:

Equation for horizontal transverse hyperbola:

Distance between foci = 

Distance between vertices = 

Eccentricity =

Center: (h, k)

First determine the value of c. Since we know the distance between the two foci is 12, we can set that equal to .

Next, use the eccentricity equation and the value of the eccentricity provided in the question to determine the value of a.

Eccentricity =

Determine the value of 

Determine the center point to identify the values of h and k. Since the y coordinate of the foci are 4, the center point will be on the same line. Hence, .

Since center point is equal distance from both foci, and we know that the distance between the foci is 12, we can conclude that 

Center point: 

Thus, the equation of the hyperbola is:

Example Question #1 : Hyperbolas

Using the information below, determine the equation of the hyperbola.

Foci:  and 

Eccentricity: 

Possible Answers:

Correct answer:

Explanation:

General Information for Hyperbola:

Equation for horizontal transverse hyperbola:

Distance between foci = 

Distance between vertices = 

Eccentricity =

Center: (h, k)

First determine the value of c. Since we know the distance between the two foci is 8, we can set that equal to .

Next, use the eccentricity equation and the value of the eccentricity provided in the question to determine the value of a.

Eccentricity =

Determine the value of 

Determine the center point to identify the values of h and k. Since the y coordinate of the foci are 8, the center point will be on the same line. Hence, .

Since center point is equal distance from both foci, and we know that the distance between the foci is 8, we can conclude that 

Center point: 

Thus, the equation of the hyperbola is:

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