Homework Help is Here – Start Your Trial Now!
Math
Trigonometry
ci at (0, -15), (0, 15) 912) 55-12) (0, 15) 1/² (@01-15) , (2, 2); eccentricity 5/4 X

ci at (0, -15), (0, 15) 912) 55-12) (0, 15) 1/² (@01-15) , (2, 2); eccentricity 5/4 X

College Algebra
College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Rational Functions And Conics
Section4.3: Conics
Problem 99E
See similar textbooks
icon
Related questions
Question
100%
Write an equation for the hyperbola
**Hyperbolas: Key Concepts and Examples** **2) y-intercepts ± 12; foci at (0, -15), (0, 15)** - The graph depicts a hyperbola centered at the origin (0,0) with its transverse axis along the y-axis. - The vertices are at (0,12) and (0,-12). - The foci are at (0,15) and (0,-15). **Handwritten Notes:** - There is a sketch of a coordinate plane with the hyperbola displaying its vertices at (0,12) and (0,-12). - The foci are marked at (0,15) and (0,-15). - An equation format: \(\frac{y^2}{144} - \frac{x^2}{b^2} = 1\) is written, indicating a vertical hyperbola. **3) vertices at (2, 10), (2, 2); eccentricity \(\frac{5}{4}\)** - The vertices are at (2,10) and (2,2), suggesting a vertical orientation of the hyperbola. - The eccentricity is given as \(\frac{5}{4}\), which is a measure of how much the conic section deviates from being circular. **Summary:** This section has focused on the properties and components of hyperbolas, including vertices, foci, and the concept of eccentricity. Understanding these fundamental parts helps in sketching and analyzing hyperbolas based on given conditions.
Transcribed Image Text:**Hyperbolas: Key Concepts and Examples** **2) y-intercepts ± 12; foci at (0, -15), (0, 15)** - The graph depicts a hyperbola centered at the origin (0,0) with its transverse axis along the y-axis. - The vertices are at (0,12) and (0,-12). - The foci are at (0,15) and (0,-15). **Handwritten Notes:** - There is a sketch of a coordinate plane with the hyperbola displaying its vertices at (0,12) and (0,-12). - The foci are marked at (0,15) and (0,-15). - An equation format: \(\frac{y^2}{144} - \frac{x^2}{b^2} = 1\) is written, indicating a vertical hyperbola. **3) vertices at (2, 10), (2, 2); eccentricity \(\frac{5}{4}\)** - The vertices are at (2,10) and (2,2), suggesting a vertical orientation of the hyperbola. - The eccentricity is given as \(\frac{5}{4}\), which is a measure of how much the conic section deviates from being circular. **Summary:** This section has focused on the properties and components of hyperbolas, including vertices, foci, and the concept of eccentricity. Understanding these fundamental parts helps in sketching and analyzing hyperbolas based on given conditions.
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
College Algebra
College Algebra
Algebra
ISBN:
9781337282291
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS