All Precalculus Resources
Example Questions
Example Question #10 : Conic Sections
Using the information below, determine the equation of the hyperbola.
Foci: and
Eccentricity:
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:
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:
All Precalculus Resources
![Learning Tools by Varsity Tutors](https://vt-vtwa-app-assets.varsitytutors.com/assets/problems/og_image_practice_problems-9cd7cd1b01009043c4576617bc620d0d5f9d58294f59b6d6556fd8365f7440cf.jpg)